{"id":23068,"date":"2023-01-30T11:41:46","date_gmt":"2023-01-30T11:41:46","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=23068"},"modified":"2024-03-15T06:23:03","modified_gmt":"2024-03-15T06:23:03","slug":"distance-between-two-points","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/distance-between-two-points","title":{"rendered":"Distance Between Two Points"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-2ce5aacc-dbcd-4f74-b07d-fe4160b26806\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/distance-between-two-points#0-distance-between-two-points-introduction>Distance between Two Points: Introduction<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/distance-between-two-points#3-what-are-the-coordinates-of-a-point>What Are the Coordinates of a Point?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/distance-between-two-points#6-derivation-of-distance-formula>Derivation of Distance Formula<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/distance-between-two-points#10-solved-examples>Solved Examples<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/distance-between-two-points#11-practice-problems>Practice Problems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/distance-between-two-points#12-frequently-asked-questions>Frequently Asked Questions<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-distance-between-two-points-introduction\">Distance between Two Points: Introduction<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Given any two points on a coordinate plane, we can find the distance between them if the coordinates of both points are known. It is a fundamental concept in geometry. Let\u2019s dive right into it!<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-two-numbers-up-to-5\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_complete_add_w5_pt.png\" alt=\"Add Two Numbers (Up to 5) Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Two Numbers (Up to 5) Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-two-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_add_numbers_1_pt.png\" alt=\"Add Two Numbers Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Two Numbers Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/calculate-the-difference-between-amounts-of-money\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/measurement_sub_word_prob_2_pt.png\" alt=\"Calculate the Difference Between Amounts of Money Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Calculate the Difference Between Amounts of Money Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/choose-the-missing-number-in-between\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/count_comp_nmbrs_in_btwn_pt.png\" alt=\"Choose the Missing Number in Between Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Choose the Missing Number in Between Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/complete-the-division-solution-where-dividend-is-between-6-9\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_div_6_to_9_b_pt.png\" alt=\"Complete the Division Solution Where Dividend is Between 6-9 Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Complete the Division Solution Where Dividend is Between 6-9 Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/complete-the-multiplication-between-fractions-and-whole-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_complete_multiplication_pt.png\" alt=\"Complete the Multiplication Between Fractions and Whole Numbers Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Complete the Multiplication Between Fractions and Whole Numbers Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/complete-the-multiplication-of-two-2-digit-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_complete_mult_1_pt.png\" alt=\"Complete the Multiplication of Two 2-Digit Numbers Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Complete the Multiplication of Two 2-Digit Numbers Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/complete-the-subtraction-between-a-mixed-number-and-a-fraction\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_complete_sub_pt.png\" alt=\"Complete the Subtraction between a Mixed Number and a Fraction Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Complete the Subtraction between a Mixed Number and a Fraction Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/convert-between-gallons-pints-quarts-and-cups-using-table\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/measurement_conversion_table_custom_capacity_pt.png\" alt=\"Convert Between Gallons, Pints, Quarts and Cups Using Table Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Convert Between Gallons, Pints, Quarts and Cups Using Table Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/convert-between-ounces-and-pounds-using-table\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/measurement_conversion_table_custom_weight_pt.png\" alt=\"Convert Between Ounces and Pounds Using Table Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Convert Between Ounces and Pounds Using Table Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-distance-between-two-points-definition\">Distance between Two Points: Definition<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We can define the distance between two points as the length of the line segment that connects the two given points. Distance between two points on the Cartesian plane can be calculated by finding the length of the line segment that joins the given coordinates.&nbsp;<\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-with-regrouping-horizontal-addition-and-subtraction\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-with-regrouping-horizontal-addition-and-subtraction.jpeg\" alt=\"Add and Subtract Two 2-Digit Numbers with Regrouping: Horizontal Addition and Subtraction Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-with-regrouping-missing-digits\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-with-regrouping-missing-digits.jpeg\" alt=\"Add and Subtract Two 2-Digit Numbers with Regrouping: Missing Digits Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-with-regrouping-missing-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-with-regrouping-missing-numbers.jpeg\" alt=\"Add and Subtract Two 2-Digit Numbers with Regrouping: Missing Numbers Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-with-regrouping-vertical-addition-and-subtraction\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-with-regrouping-vertical-addition-and-subtraction.jpeg\" alt=\"Add and Subtract Two 2-Digit Numbers with Regrouping: Vertical Addition and Subtraction Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-without-regrouping-horizontal-addition-and-subtraction\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-without-regrouping-horizontal-addition-and-subtraction.jpeg\" alt=\"Add and Subtract Two 2-Digit Numbers without Regrouping: Horizontal Addition and Subtraction Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-without-regrouping-horizontal-timed-practice\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-without-regrouping-horizontal-timed-practice.jpeg\" alt=\"Add and Subtract Two 2-Digit Numbers without Regrouping: Horizontal Timed Practice\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-without-regrouping-missing-digits\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-without-regrouping-missing-digits.jpeg\" alt=\"Add and Subtract Two 2-Digit Numbers without Regrouping: Missing Digits Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-without-regrouping-missing-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-without-regrouping-missing-numbers.jpeg\" alt=\"Add and Subtract Two 2-Digit Numbers without Regrouping: Missing Numbers Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-without-regrouping-vertical-addition-and-subtraction\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-without-regrouping-vertical-addition-and-subtraction.jpeg\" alt=\"Add and Subtract Two 2-Digit Numbers without Regrouping: Vertical Addition and Subtraction Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-without-regrouping-vertical-timed-practice\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" 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10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-what-is-the-distance-between-two-points-\">What Is the Distance between Two Points?&nbsp;<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">There is only one line passing through two points. So, the distance between two points can be calculated by finding the length of the line segment connecting the two points.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, if P and Q are two points and PQ $= 8$ feet, it means that the distance between the points P and Q is 8 feet.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"395\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/a-line-segment-having-8-feet-length.png\" alt=\"A line segment having 8 feet length\" class=\"wp-image-40964\" title=\"A line segment having 8 feet length\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/a-line-segment-having-8-feet-length.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/a-line-segment-having-8-feet-length-300x191.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The distance between two points is the length of the line segment joining them. Since the length of the line segment cannot be negative, the distance between two points is always positive.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The distance from the point A to B is the same as the distance from B to A.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">NOTE: The shortest distance between two points is the straight line joining them.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"433\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/shortest-distance-between-two-points-is-a-straight-line.png\" alt=\"Shortest distance between two points is a straight line\" class=\"wp-image-40965\" title=\"Shortest distance between two points is a straight line\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/shortest-distance-between-two-points-is-a-straight-line.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/shortest-distance-between-two-points-is-a-straight-line-300x210.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-what-are-the-coordinates-of-a-point\">What Are the Coordinates of a Point?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In Euclidean geometry, the position of points is defined by their coordinates along the X- axis and Y-axis. Therefore, the coordinates of a point is the ordered pair that is used to identify the location of that point in the coordinate plane.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"447\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/coordinates-of-point-a-in-cartesian-plane.png\" alt=\"Coordinates of point A in Cartesian plane\" class=\"wp-image-40967\" title=\"Coordinates of point A in Cartesian plane\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/coordinates-of-point-a-in-cartesian-plane.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/coordinates-of-point-a-in-cartesian-plane-300x216.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the above figure, the coordinates of point A are&nbsp; (x,y). This means that the point A is x units away from the y-axis and y units away from the x-axis.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Coordinates of a point on the x-axis are of the form (x, 0), where x is the distance of the point from the origin.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Coordinates of a point on the y-axis are of the form (0, y), where y is the distance of the point from the origin.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"555\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/plotting-a-point-in-a-cartesian-plane.png\" alt=\"Plotting a point in a Cartesian plane\" class=\"wp-image-40968\" title=\"Plotting a point in a Cartesian plane\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/plotting-a-point-in-a-cartesian-plane.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/plotting-a-point-in-a-cartesian-plane-300x269.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-how-to-find-the-distance-between-two-points\">How to Find the Distance between Two Points?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To find the distance between two points, we find the distance between two coordinates corresponding to those points using the distance formula. For any point in the 2-D Cartesian plane, we apply the 2-D distance formula or the Euclidean distance formula.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-the-distance-between-two-points-formula\">The Distance between Two Points Formula<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If the coordinates of the points are P$(\\text{x}_{1},\\text{y}_{1})$ and Q$(\\text{x}_{2},\\text{y}_{2})$, then the distance between P and Q is given by&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">PQ $=\\sqrt{(\\text{x}_{2} \u2212 \\text{x}_{1})^{2} + (\\text{y}_{2} \u2212 \\text{y}_{1})^{2}}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-derivation-of-distance-formula\">Derivation of Distance Formula<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Suppose we have two points A$(\\text{x}_{1},\\text{y}_{1})$ and B$(\\text{x}_{2},\\text{y}_{2})$ in the coordinate plane. We have to find the distance between them.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"618\" height=\"494\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/distance-between-two-points-using-distance-formula.png\" alt=\"Distance between two points using distance formula\" class=\"wp-image-40969\" title=\"Distance between two points using distance formula\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/distance-between-two-points-using-distance-formula.png 618w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/distance-between-two-points-using-distance-formula-300x240.png 300w\" sizes=\"auto, (max-width: 618px) 100vw, 618px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">What do we know?&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">AC and BD are perpendicular to the x-axis.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">AB is parallel to the x-axis.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Coordinates: A$(\\text{x}_{1},\\text{y}_{1})$ and B$(\\text{x}_{2},\\text{y}_{2})$, $C(\\text{x}_{1},0)$ and D$(\\text{x}_{2},0)$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Distance between the points A and B is calculated as follows:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">C and D are the points on the x-axis.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\text{AM} = \\text{CD} = \\text{OD} \u2013 \\text{OC} = \\text{x}_{2} \u2013 \\text{x}_{1}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Similarly, $\\text{AC} = \\text{MD}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\text{AC} = \\text{MD} = \\text{BD} \u2013 \\text{AC} = \\text{y}_{2} \u2013 \\text{y}_{1}$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"334\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/derivation-of-distance-formula.png\" alt=\"Derivation of distance formula  \" class=\"wp-image-40970\" title=\"Derivation of distance formula  \" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/derivation-of-distance-formula.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/derivation-of-distance-formula-300x162.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">By Pythagoras\u2019 theorem,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$PQ^{2} = PR^{2} + QR^{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">PQ $=\\sqrt{(\\text{x}_{2} \u2212 \\text{x}_{1})^{2} + (\\text{y}_{2} \u2212 \\text{y}_{1})^{2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, distance between two points $(\\text{x}_{1},\\text{y}_{1})$ and $(\\text{x}_{2},\\text{y}_{2})$ is given by:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">PQ $=\\sqrt{(\\text{x}_{2} \u2212 \\text{x}_{1})^{2} + (\\text{y}_{2} \u2212 \\text{y}_{1})^{2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The final formula remains the same, irrespective of which quadrants A and B lie in.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We can summarize the formula in a picture as:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"378\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/distance-formula-to-find-distance-between-two-points.png\" alt=\"Distance formula to find distance between two points\" class=\"wp-image-40971\" title=\"Distance formula to find distance between two points\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/distance-formula-to-find-distance-between-two-points.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/distance-formula-to-find-distance-between-two-points-300x183.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 1:<\/strong> The distance between the points P(3, 0) and Q(0, 4) is<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">PQ $=\\sqrt{(4 \u2212 0)^{2} + (0 \u2212 3)^{2}} = \\sqrt{16 + 9} = \\sqrt{25} = 5$ units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 2: <\/strong>R(2, 5) and S(1, 2)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">RS $=\\sqrt{(1 \u2212 2)^{2}+(2 \u2212 5)^{2}} = \\sqrt{1 + 9} = \\sqrt{10}$ units<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-distance-of-a-point-from-the-origin\">Distance of a Point from the Origin<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Suppose a point P(x, y) in the xy\u2013plane as shown in the figure below:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"382\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/distance-of-a-point-from-the-origin.png\" alt=\"Distance of a point from the origin\" class=\"wp-image-40972\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/distance-of-a-point-from-the-origin.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/distance-of-a-point-from-the-origin-300x185.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The distance between point A and the origin is OA.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Point A is x units away from the y-axis and y units away from the x-axis.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Using Pythagoras\u2019 theorem, we get<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">OA $=\\sqrt{(x \u2212 0)^{2} + (y \u2212 0)^{2}} = \\sqrt{x^{2} + y^{2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, the distance between any point (x,y) in xy-plane and the origin (0,0) is given by: d $= \\sqrt{x^{2} + y^{2}}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-distance-between-two-points-using-pythagoras%E2%80%99-theorem\">Distance between Two Points: Using Pythagoras\u2019 Theorem<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Consider the following example.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A boy started from point A and walked west for 12 miles. He then turned to the north and walked for 5 miles more. We have to calculate the shortest distance between the initial position and final position.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A pictorial representation of the above situation is:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"411\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/distance-between-two-points-using-pythagoras-theorem.png\" alt=\"Distance between two points using Pythagoras\u2019 theorem\" class=\"wp-image-40973\" title=\"Distance between two points using Pythagoras\u2019 theorem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/distance-between-two-points-using-pythagoras-theorem.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/distance-between-two-points-using-pythagoras-theorem-300x199.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The initial position is A and the final position is C. The distance between points A and B is 12 miles and between points B and C is 5 miles. Here, triangle ABC is a right triangle.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The shortest distance between points A and C is given by AC. This distance is calculated using the Pythagoras theorem as follows:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$AC = \\sqrt{AB^{2} + BC^{2}} = \\sqrt{12^{2} + 5^{2}} = \\sqrt{144 + 25} = \\sqrt{169} = 13$ miles<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In this article, we learned about the distance between two points. The distance between two points can be calculated by measuring the length of the line segment. To read more such informative articles on other concepts, do visit our <a href=\"https:\/\/www.splashlearn.com\/ela-games\">website<\/a>. We, at SplashLearn, are on a mission to make learning fun and interactive for all students.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-solved-examples\">Solved Examples<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>1. What is the distance between <\/strong><strong>(0,0)<\/strong><strong> and <\/strong><strong>(3,4)<\/strong><strong>?<\/strong><strong>&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong> The distance between <strong>(0,0)<\/strong><strong> <\/strong>and <strong>(x,y)<\/strong><strong> <\/strong>is given by: $\\sqrt{x^{2} + y^{2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The distance between <strong>(0,0)<\/strong><strong> <\/strong>and <strong>(3,4)<\/strong><strong> <\/strong>is given by: $\\sqrt{3^{2} + 4^{2}} = \\sqrt{9 + 16} = \\sqrt{25} = 5$ units.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>2. Find the distance between the points <\/strong>$( \u2212 1,2)$<strong> and <\/strong>$(4, \u2212 8)$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong> The distance between the points $( \u2212 1,2)<strong> and <\/strong>$(4, \u2212 8)$<strong> <\/strong>is given by:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\sqrt{(4 \u2212 ( \u2212 1))^{2} + ( \u2212 8 \u2212 2)^{2}} =\\sqrt{5^{2} + ( \u2212 10)^{2}} = \\sqrt{25 + 100} = \\sqrt{125} = 5\\sqrt{5}$ units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>3. If the distance between the points <\/strong>$(4, 4)$<strong> and <\/strong>$(1, a)$<strong> is 5 units, then find the value of a.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution<\/strong>: Distance between the points $(4, 4)$<strong> <\/strong>and<strong> <\/strong>$(1, a) = \\sqrt{(1 \u2212 4)^{2} + (a \u2212 4)^{2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$5 = \\sqrt{(1 \u2212 4)^{2} + (a \u2212 4)^{2}} = \\sqrt{( \u2212 3)^{2} + (a \u2212 4)^{2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">On squaring both the sides, we get the equation for distance between two points as<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$25 = 9 + (a \u2212 4)^{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$25 \u2212 9 = (a \u2212 4)^{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$16 = (a \u2212 4)^{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Taking square root<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$4 = a \u2212 4$&nbsp; or&nbsp; $\u2212 4 = a \u2212 4$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$a = 8$&nbsp; or $a = 0$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>4. Find a point on the <\/strong>x<strong> axis that is equidistant from the points <\/strong>$(1,\u2212 4)$<strong> and <\/strong>$( \u2212 3,4)$<strong>.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong> Let the point on x axis be B$(x,0)$ and let A$(1, \u2212 4)$<strong> <\/strong>and<strong> <\/strong>C$( \u2212 3,4)$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$AB = BC \\Rightarrow AB^{2} = BC^{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$(x \u2212 1)^{2} + (0 \u2212(\u2212 4))^{2} =(x \u2212( \u22123))^{2} + (0 \u2212 4)^{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$(x \u22121)^{2} + 16 = (x + 3)^{2} + 16$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$(x \u2212 1)^{2} \u2212 (x + 3)^{2} = 16 \u2212 16$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x^{2} \u2212 2x + 1 \u2212 (x^{2} + 6x + 9) = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x^{2} \u2212 2x + 1 \u2212 9 \u2212 x^{2} \u2212 6x = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\u2212 8x \u2212 8 = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\u2212 8x = 8$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x = \\frac{\u22128}{8} = \u22121$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The point is $( \u22121,0)$<strong>.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>5. Amaya traveled 20 miles to the west and then 21 miles to the north. Calculate the shortest distance between the initial and final point?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong> Assuming $AB = 20$ mi and $BC = 21$ mi<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The shortest distance $= AC =$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= \\sqrt{AB^{2} + BC^{2}} = \\sqrt{20^{2} + 21^{2}} = \\sqrt{400 + 441} = \\sqrt{841} = 29$ mi<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-practice-problems\">Practice Problems<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Distance Between Two Points<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">If the distance between the origin and $(a, 8)$ is 17 units, then find the value of $a$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">0<\/div><div class=\"spq_answer_block\" data-value=\"1\">15<\/div><div class=\"spq_answer_block\" data-value=\"2\">21<\/div><div class=\"spq_answer_block\" data-value=\"3\">29<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 15<br\/>The distance between $(0,0)$ and $(a, 8)$ is given by: $\\sqrt{a^{2} + 8^{2}} = 17$<br>\r\nOn squaring, we get $a^{2} + 64 = 289$<br>\r\n$\\Rightarrow a^{2} = 289$ $-$ $64 \\Rightarrow a^{2} = 225 \\Rightarrow a = 15$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">The distance of $(-$$5,8)$ from x-axis is:<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$8$ units<\/div><div class=\"spq_answer_block\" data-value=\"1\">$-8$ units<\/div><div class=\"spq_answer_block\" data-value=\"2\">$-5$ units<\/div><div class=\"spq_answer_block\" data-value=\"3\">$5$ units<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $8$ units<br\/>The distance of $(-$$5,8)$ from x-axis is the distance between $(-$$5,8)$ and $(-$$5,0)$.<br>\r\nThe distance of $(-$$5,8)$ from x-axis $= |8$$-$$0| = 8$ units.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">The distance of $(-$$2,-$$10)$ from y-axis is:<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$10$ units<\/div><div class=\"spq_answer_block\" data-value=\"1\">$-10$ units<\/div><div class=\"spq_answer_block\" data-value=\"2\">$-2$ units<\/div><div class=\"spq_answer_block\" data-value=\"3\">$2$ units<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $2$ units<br\/>The distance of $(-$$2,-$$10)$ from y-axis $= | -2|$ units $= 2$ units<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Find half the length of the line segment joining the points $(2,3)$ and $(5,7)$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$2$ units<\/div><div class=\"spq_answer_block\" data-value=\"1\">$2.5$ units<\/div><div class=\"spq_answer_block\" data-value=\"2\">$5$ units<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\sqrt{13}$ units<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $2.5$ units<br\/>The distance between the points $(2,3)$ and $(5,7)$ is<br>\r\n$\\sqrt{(5 - 2)^{2} + (7 - 3)^{2}} = \\sqrt{9 + 16} = \\sqrt{25} = 5$ units. Half the distance is 2.5 units.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Shyna traveled east by bus and west by car. If the distance covered by bus is 24 km and the shortest distance is 25 km, then what is the distance covered by car?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">1 km<\/div><div class=\"spq_answer_block\" data-value=\"1\">11 km<\/div><div class=\"spq_answer_block\" data-value=\"2\">7 km<\/div><div class=\"spq_answer_block\" data-value=\"3\">10 km<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 7 km<br\/>Let the distance covered by car be $x$ km.<br>\r\nShortest distance $= \\sqrt{24^{2} + x^{2}} \\Rightarrow 25 = \\sqrt{24^{2} + x^{2}}$<br>\r\nSquaring both the sides, we get $625 = 576 + x^{2} \\Rightarrow x^{2} = 49 \\Rightarrow x = 7$<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        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$$\\\\sqrt{a^{2} + 8^{2}} = 17$$<br>\r\nOn squaring, we get $$a^{2} + 64 = 289$$<br>\r\n$$\\\\Rightarrow a^{2} = 289$$ $$-$$ $$64 \\\\Rightarrow a^{2} = 225 \\\\Rightarrow a = 15$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"21\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The distance between $$(0,0)$$ and $$(a, 8)$$ is given by: $$\\\\sqrt{a^{2} + 8^{2}} = 17$$<br>\r\nOn squaring, we get $$a^{2} + 64 = 289$$<br>\r\n$$\\\\Rightarrow a^{2} = 289$$ $$-$$ $$64 \\\\Rightarrow a^{2} = 225 \\\\Rightarrow a = 15$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"29\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The distance between $$(0,0)$$ and $$(a, 8)$$ is given by: $$\\\\sqrt{a^{2} + 8^{2}} = 17$$<br>\r\nOn squaring, we get $$a^{2} + 64 = 289$$<br>\r\n$$\\\\Rightarrow a^{2} = 289$$ $$-$$ $$64 \\\\Rightarrow a^{2} = 225 \\\\Rightarrow a = 15$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"15\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The distance between $$(0,0)$$ and $$(a, 8)$$ is given by: $$\\\\sqrt{a^{2} + 8^{2}} = 17$$<br>\r\nOn squaring, we get $$a^{2} + 64 = 289$$<br>\r\n$$\\\\Rightarrow a^{2} = 289$$ $$-$$ $$64 \\\\Rightarrow a^{2} = 225 \\\\Rightarrow a = 15$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The distance between $$(0,0)$$ and $$(a, 8)$$ is given by: $$\\\\sqrt{a^{2} + 8^{2}} = 17$$<br>\r\nOn squaring, we get $$a^{2} + 64 = 289$$<br>\r\n$$\\\\Rightarrow a^{2} = 289$$ $$-$$ $$64 \\\\Rightarrow a^{2} = 225 \\\\Rightarrow a = 15$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The distance of $$(-$$$$5,8)$$ from x-axis is:\",\n                    \"text\": \"The distance of $$(-$$$$5,8)$$ from x-axis is:\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The distance of $$(-$$$$5,8)$$ from x-axis is the distance between $$(-$$$$5,8)$$ and $$(-$$$$5,0)$$.<br>\r\nThe distance of $$(-$$$$5,8)$$ from x-axis $$= |8$$$$-$$$$0| = 8$$ units.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$-8$$ units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The distance of $$(-$$$$5,8)$$ from x-axis is the distance between $$(-$$$$5,8)$$ and $$(-$$$$5,0)$$.<br>\r\nThe distance of $$(-$$$$5,8)$$ from x-axis $$= |8$$$$-$$$$0| = 8$$ units.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$-5$$ units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The distance of $$(-$$$$5,8)$$ from x-axis is the distance between $$(-$$$$5,8)$$ and $$(-$$$$5,0)$$.<br>\r\nThe distance of $$(-$$$$5,8)$$ from x-axis $$= |8$$$$-$$$$0| = 8$$ units.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$5$$ units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The distance of $$(-$$$$5,8)$$ from x-axis is the distance between $$(-$$$$5,8)$$ and $$(-$$$$5,0)$$.<br>\r\nThe distance of $$(-$$$$5,8)$$ from x-axis $$= |8$$$$-$$$$0| = 8$$ units.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$8$$ units\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The distance of $$(-$$$$5,8)$$ from x-axis is the distance between $$(-$$$$5,8)$$ and $$(-$$$$5,0)$$.<br>\r\nThe distance of $$(-$$$$5,8)$$ from x-axis $$= |8$$$$-$$$$0| = 8$$ units.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The distance of $$(-$$$$5,8)$$ from x-axis is the distance between $$(-$$$$5,8)$$ and $$(-$$$$5,0)$$.<br>\r\nThe distance of $$(-$$$$5,8)$$ from x-axis $$= |8$$$$-$$$$0| = 8$$ units.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The distance of $$(-$$$$2,-$$$$10)$$ from y-axis is:\",\n                    \"text\": \"The distance of $$(-$$$$2,-$$$$10)$$ from y-axis is:\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The distance of $$(-$$$$2,-$$$$10)$$ from y-axis $$= | -2|$$ units $$= 2$$ units\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$10$$ units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The distance of $$(-$$$$2,-$$$$10)$$ from y-axis $$= | -2|$$ units $$= 2$$ units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$-10$$ units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The distance of $$(-$$$$2,-$$$$10)$$ from y-axis $$= | -2|$$ units $$= 2$$ units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$-2$$ units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The distance of $$(-$$$$2,-$$$$10)$$ from y-axis $$= | -2|$$ units $$= 2$$ units\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$2$$ units\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The distance of $$(-$$$$2,-$$$$10)$$ from y-axis $$= | -2|$$ units $$= 2$$ units\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The distance of $$(-$$$$2,-$$$$10)$$ from y-axis $$= | -2|$$ units $$= 2$$ units\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find half the length of the line segment joining the points $$(2,3)$$ and $$(5,7)$$.\",\n                    \"text\": \"Find half the length of the line segment joining the points $$(2,3)$$ and $$(5,7)$$.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The distance between the points $$(2,3)$$ and $$(5,7)$$ is<br>\r\n$$\\\\sqrt{(5 - 2)^{2} + (7 - 3)^{2}} = \\\\sqrt{9 + 16} = \\\\sqrt{25} = 5$$ units. Half the distance is 2.5 units.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$2$$ units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The distance between the points $$(2,3)$$ and $$(5,7)$$ is<br>\r\n$$\\\\sqrt{(5 - 2)^{2} + (7 - 3)^{2}} = \\\\sqrt{9 + 16} = \\\\sqrt{25} = 5$$ units. Half the distance is 2.5 units.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$5$$ units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The distance between the points $$(2,3)$$ and $$(5,7)$$ is<br>\r\n$$\\\\sqrt{(5 - 2)^{2} + (7 - 3)^{2}} = \\\\sqrt{9 + 16} = \\\\sqrt{25} = 5$$ units. Half the distance is 2.5 units.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\sqrt{13}$$ units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The distance between the points $$(2,3)$$ and $$(5,7)$$ is<br>\r\n$$\\\\sqrt{(5 - 2)^{2} + (7 - 3)^{2}} = \\\\sqrt{9 + 16} = \\\\sqrt{25} = 5$$ units. Half the distance is 2.5 units.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$2.5$$ units\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The distance between the points $$(2,3)$$ and $$(5,7)$$ is<br>\r\n$$\\\\sqrt{(5 - 2)^{2} + (7 - 3)^{2}} = \\\\sqrt{9 + 16} = \\\\sqrt{25} = 5$$ units. Half the distance is 2.5 units.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The distance between the points $$(2,3)$$ and $$(5,7)$$ is<br>\r\n$$\\\\sqrt{(5 - 2)^{2} + (7 - 3)^{2}} = \\\\sqrt{9 + 16} = \\\\sqrt{25} = 5$$ units. Half the distance is 2.5 units.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Shyna traveled east by bus and west by car. If the distance covered by bus is 24 km and the shortest distance is 25 km, then what is the distance covered by car?\",\n                    \"text\": \"Shyna traveled east by bus and west by car. If the distance covered by bus is 24 km and the shortest distance is 25 km, then what is the distance covered by car?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Let the distance covered by car be $$x$$ km.<br>\r\nShortest distance $$= \\\\sqrt{24^{2} + x^{2}} \\\\Rightarrow 25 = \\\\sqrt{24^{2} + x^{2}}$$<br>\r\nSquaring both the sides, we get $$625 = 576 + x^{2} \\\\Rightarrow x^{2} = 49 \\\\Rightarrow x = 7$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1 km\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let the distance covered by car be $$x$$ km.<br>\r\nShortest distance $$= \\\\sqrt{24^{2} + x^{2}} \\\\Rightarrow 25 = \\\\sqrt{24^{2} + x^{2}}$$<br>\r\nSquaring both the sides, we get $$625 = 576 + x^{2} \\\\Rightarrow x^{2} = 49 \\\\Rightarrow x = 7$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"11 km\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let the distance covered by car be $$x$$ km.<br>\r\nShortest distance $$= \\\\sqrt{24^{2} + x^{2}} \\\\Rightarrow 25 = \\\\sqrt{24^{2} + x^{2}}$$<br>\r\nSquaring both the sides, we get $$625 = 576 + x^{2} \\\\Rightarrow x^{2} = 49 \\\\Rightarrow x = 7$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10 km\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let the distance covered by car be $$x$$ km.<br>\r\nShortest distance $$= \\\\sqrt{24^{2} + x^{2}} \\\\Rightarrow 25 = \\\\sqrt{24^{2} + x^{2}}$$<br>\r\nSquaring both the sides, we get $$625 = 576 + x^{2} \\\\Rightarrow x^{2} = 49 \\\\Rightarrow x = 7$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"7 km\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Let the distance covered by car be $$x$$ km.<br>\r\nShortest distance $$= \\\\sqrt{24^{2} + x^{2}} \\\\Rightarrow 25 = \\\\sqrt{24^{2} + x^{2}}$$<br>\r\nSquaring both the sides, we get $$625 = 576 + x^{2} \\\\Rightarrow x^{2} = 49 \\\\Rightarrow x = 7$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Let the distance covered by car be $$x$$ km.<br>\r\nShortest distance $$= \\\\sqrt{24^{2} + x^{2}} \\\\Rightarrow 25 = \\\\sqrt{24^{2} + x^{2}}$$<br>\r\nSquaring both the sides, we get $$625 = 576 + x^{2} \\\\Rightarrow x^{2} = 49 \\\\Rightarrow x = 7$$\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"12-frequently-asked-questions\">Frequently Asked Questions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-9b2c1eff-0f44-40ec-b96d-34258844180b\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-9b2c1eff-0f44-40ec-b96d-34258844180b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9b2c1eff-0f44-40ec-b96d-34258844180b\"><strong>What is the distance between two points in a 3D plane?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-9b2c1eff-0f44-40ec-b96d-34258844180b\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If the coordinates of two points in a 3D plane are P$(\\text{x}_{1}, \\text{y}_{1}, \\text{z}_{1})$ and Q$(\\text{x}_{2}, \\text{y}_{2}, \\text{z}_{2})$, the distance between the points P and Q is given by&nbsp;PQ $= \\sqrt{(x_{2} \u2212 x_{1})^{2} + (y_{2} \u2212 y_{1})^{2} + (z_{2} \u2212 z_{1})^{2}}$<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-9b2c1eff-0f44-40ec-b96d-34258844180b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9b2c1eff-0f44-40ec-b96d-34258844180b\"><strong>What is the shortest distance between two points?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-9b2c1eff-0f44-40ec-b96d-34258844180b\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The shortest distance between two points is the length of the straight line that connects both the points. We use the distance formula to find this distance using the coordinates given in a two-dimensional plane.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-9b2c1eff-0f44-40ec-b96d-34258844180b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9b2c1eff-0f44-40ec-b96d-34258844180b\"><strong>How can one find the vertical distance between two points?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-9b2c1eff-0f44-40ec-b96d-34258844180b\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The vertical distance between two points is calculated by the difference of the y coordinates of the two points, i.e., vertical distance between two points, $|(y_{2} \u2212 y_{1})|$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-9b2c1eff-0f44-40ec-b96d-34258844180b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9b2c1eff-0f44-40ec-b96d-34258844180b\"><strong>How to find the horizontal distance between two points?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-9b2c1eff-0f44-40ec-b96d-34258844180b\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The vertical distance between two points is calculated by the difference of the y coordinates of the two points, i.e., vertical distance between two points, $(\\text{y}_{2} \u2212 \\text{y}_{1})$ where $(\\text{x}_{1}, \\text{y}_{1})$ and $(\\text{x}_{2},\\text{y}_{2})$ are the coordinates of the points.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-9b2c1eff-0f44-40ec-b96d-34258844180b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9b2c1eff-0f44-40ec-b96d-34258844180b\"><strong>Can we change the order of the points in the distance formula?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-9b2c1eff-0f44-40ec-b96d-34258844180b\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Yes, we can change the order of points in the distance formula. We can also write the formula as $\\sqrt{(x_{1} \u2212 x_{2})^{2} + (y_{1} \u2212 y_{2})^{2}} = \\sqrt{(x_{2} \u2212 x_{1})^{2} + (y_{2} \u2212 y_{1})^{2}}$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-5-9b2c1eff-0f44-40ec-b96d-34258844180b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9b2c1eff-0f44-40ec-b96d-34258844180b\"><strong>What is the driving distance between two points or places?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-5-9b2c1eff-0f44-40ec-b96d-34258844180b\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The driving distance generally refers to the distance when traveling by car. For example, the driving distance from Chicago to Orlando (is 1179 miles.<\/p>\n\n<\/div><\/div>\n<\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"13-related-articles\">Related Articles<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/coordinate-plane\">Coordinate Plane<\/a><\/li>\n\n\n\n<li class=\"eplus-wrapper\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/point\">Point<\/a><\/li>\n\n\n\n<li class=\"eplus-wrapper\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/line-segment\">Line Segment<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Distance between Two Points: Introduction Given any two points on a coordinate plane, we can find the distance between them if the coordinates of both points are known. It is a fundamental concept in geometry. Let\u2019s dive right into it! Recommended Games Add Two Numbers (Up to 5) Game Play Add Two Numbers Game Play &#8230; <a title=\"Distance Between Two Points\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/distance-between-two-points\" aria-label=\"More on Distance Between Two Points\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-23068","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/23068","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=23068"}],"version-history":[{"count":34,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/23068\/revisions"}],"predecessor-version":[{"id":40974,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/23068\/revisions\/40974"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=23068"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=23068"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=23068"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}