{"id":29364,"date":"2023-05-12T18:42:16","date_gmt":"2023-05-12T18:42:16","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=29364"},"modified":"2023-10-04T11:41:23","modified_gmt":"2023-10-04T11:41:23","slug":"distance-between-point-and-line-formula-definition-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/distance-of-a-point-from-a-line","title":{"rendered":"Distance between Point and Line: Formula, Definition, Examples"},"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-3f4b450e-2bc9-40fe-b347-ac02cd4268ed\" 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-of-a-point-from-a-line#0-what-is-the-distance-between-a-point-and-a-line>What Is the Distance between a Point and a Line?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/distance-of-a-point-from-a-line#1-distance-from-a-point-to-a-line-definition-in-geometry>Distance from a Point to a Line Definition in Geometry<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/distance-of-a-point-from-a-line#3-how-to-find-the-distance-between-point-and-line>How to Find the Distance Between Point and Line<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/distance-of-a-point-from-a-line#8-solved-examples-on-distance-between-point-and-line>Solved Examples on Distance between Point and Line<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/distance-of-a-point-from-a-line#9-practice-problems-on-distance-between-point-and-line>Practice Problems on Distance Between Point and Line<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/distance-of-a-point-from-a-line#10-frequently-asked-questions-on-the-distance-between-point-and-line>Frequently Asked Questions on the Distance between Point and Line<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-the-distance-between-a-point-and-a-line\">What Is the Distance between a Point and a Line?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>The distance between point and line is the shortest distance between the point and the straight line.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Consider a line BF and a point A as shown in the diagram below. We can draw an infinite number of line segments from the line to the point A. So, what is the actual distance between the given line and the point A?<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"347\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/distance-between-a-point-and-a-line.png\" alt=\"Distance between a point and a line\" class=\"wp-image-34589\" title=\"Distance between a point and a line\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/distance-between-a-point-and-a-line.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/distance-between-a-point-and-a-line-300x168.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">It is the shortest distance from A to the line. How can we find this shortest distance? <strong>The shortest distance from a point and a line is the length of the perpendicular drawn from the point to the line. <\/strong>Thus, the line segment AD defines the distance between the point and a line.&nbsp;<\/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-and-mark-the-sum-on-the-number-line\" 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_where_sum_pt.png\" alt=\"Add and Mark the Sum on the Number Line 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 and Mark the Sum on the Number Line 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-fractions-with-the-aid-of-a-number-line\" 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_add_like_frac_sum_greater_than_1_nl_pt.png\" alt=\"Add Fractions WIth the Aid of a Number LIne 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 Fractions WIth the Aid of a Number LIne 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-like-fractions-using-number-lines\" 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_add_like_frac_sum_upto_1_nl_pt.png\" alt=\"Add Like Fractions using Number Lines 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 Like Fractions using Number Lines 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-the-mixed-number-and-the-fraction-on-a-number-line\" 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_add_nl_pt.png\" alt=\"Add the Mixed Number and the Fraction on a Number Line 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 the Mixed Number and the Fraction on a Number Line 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\/analyze-and-represent-data-using-line-plots\" 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\/data_analyze_represent_data_2_pt.png\" alt=\"Analyze and Represent Data Using Line Plots 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\">Analyze and Represent Data Using Line Plots 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\/analyze-data-using-line-plots\" 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\/data_analyze_data_2_pt.png\" alt=\"Analyze Data Using Line Plots 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\">Analyze Data Using Line Plots 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\/answer-how-many-more-or-less-using-line-plots\" 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\/data_less_more_lp_pt.png\" alt=\"Answer How Many More or Less using line plots 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\">Answer How Many More or Less using line plots 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\/arrange-the-decimal-numbers-from-smallest-to-greatest\" 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\/decimals_order_dec_2_pt.png\" alt=\"Arrange the Decimal Numbers From Smallest to Greatest 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\">Arrange the Decimal Numbers From Smallest to Greatest 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\/change-decimals-from-word-form-to-fraction-form\" 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\/decimals_convert_words_to_frac_tenths_pt.png\" alt=\"Change Decimals from Word Form to Fraction Form 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\">Change Decimals from Word Form to Fraction Form 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-decimal-number-represented-on-the-number-line\" 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\/decimals_identify_dec_nl_hun_pt.png\" alt=\"Choose the Decimal Number Represented on The Number Line 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 Decimal Number Represented on The Number Line 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-from-a-point-to-a-line-definition-in-geometry\">Distance from a Point to a Line Definition in Geometry<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The <strong>distance between point and line<\/strong> is the shortest distance between the point and a point on the line. The length of a perpendicular drawn from a point to a point on the line defines the shortest distance between them.&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-using-number-line\" 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-using-number-line.jpeg\" alt=\"Add Using Number Line 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-with-10-missing-number-using-number-line\" 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-with-10-missing-number-using-number-line.jpeg\" alt=\"Add with 10 Missing Number Using Number Line\">\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-with-10-using-number-line\" 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-with-10-using-number-line.jpeg\" alt=\"Add with 10 Using Number Line\">\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\/addition-sentences-using-number-line\" 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\/addition-sentences-using-number-line.jpeg\" alt=\"Addition Sentences Using Number Line 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\/commutative-property-of-addition-on-number-line\" 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\/commutative-property-of-addition-on-number-line.jpeg\" alt=\"Commutative Property of Addition on Number Line 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\/compare-fractions-using-number-line\" 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\/compare-fractions-using-number-line.jpeg\" alt=\"Compare Fractions Using Number Line 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\/comparing-decimals-on-a-number-line\" 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\/comparing-decimals-on-a-number-line.jpeg\" alt=\"Comparing Decimals on a Number Line 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\/compose-from-given-shapes\" 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\/compose-from-given-shapes.jpeg\" alt=\"Compose From Given Shapes 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\/count-on-the-number-line-to-add\" 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\/count-on-the-number-line-to-add.jpeg\" alt=\"Count on the Number Line to Add\">\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\/count-on-the-number-line-to-find-the-missing-number\" 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\/count-on-the-number-line-to-find-the-missing-number.jpeg\" alt=\"Count on the Number Line to Find the Missing Number\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-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=\"2-distance-from-point-to-line-formula\">Distance from Point to Line Formula<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The <strong>distance between point and line<\/strong> for a line $Ax + By + C = 0$ and a point with the coordinates $(x\u2080, y\u2080)$ is calculated by the following formula&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$d = \\frac{| Ax\u2080 + By\u2080 + C |}{\\sqrt{A\u00b2 + B\u00b2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">where,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A, B, and C are real numbers.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A and B cannot be equal to zero.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The formula has an absolute zero or modulus sign in the numerator which indicates that the value of the numerator would always be a positive number or zero.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-how-to-find-the-distance-between-point-and-line\">How to Find the Distance Between Point and Line<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 1: <\/strong>Compare the given equation of a line with the standard equation $Ax + By + C = 0$ to find the values of A, B, and C.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 2: <\/strong>Compare the coordinates of the given point with $(x\u2081, y\u2081)$ to find the values of $x\u2081$ and $y\u2081$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 3: <\/strong>Substitute the values in the formula<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$d = Ax\u2081 + By\u2081 + CA\u00b2 + B\u00b2$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-perpendicular-distance-from-point-to-line\">Perpendicular Distance from Point to Line<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The shortest <strong>distance between point and line<\/strong> is calculated by finding the length of the perpendicular drawn from the point to the line.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Consider the line <em>l<\/em>: $Ax + By + C = 0$ and point $P(x\u2081, y\u2081)$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Note that PQ is the perpendicular from point P to line l. Let l$(PQ) = d$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"661\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/perpendicular-distance-between-point-and-line.png\" alt=\"Perpendicular distance between point and line\" class=\"wp-image-34591\" title=\"Perpendicular distance between point and line\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/perpendicular-distance-between-point-and-line.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/perpendicular-distance-between-point-and-line-281x300.png 281w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">M and N are the points of intersection of the line on the x-axis and y-axis.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">M is the y-intercept of line l. Putting $x = 0$ in $Ax + By + C = 0$, we get $y = \\;-\\;\\frac{C}{B}$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, $M \\equiv (0, \\;-\\;\\frac{C}{B})$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">N is the x-intercept of line l. Putting $y = 0$ in $Ax + By + C = 0$, we get $x = \\;-\\;\\frac{C}{A}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, $N \\equiv (\\;-\\;\\frac{C}{A},\\; 0)$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, PQ is the height of the&nbsp; triangle PMN. We use the formula of area of triangle and the distance formula to derive the formula for perpendicular distance between point and line.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-derivation-of-the-distance-from-point-to-line\">Derivation of the Distance from Point to Line<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We have&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">l: $Ax + By + C = 0$ and $P(x\u2081,\\; y\u2081)$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$M \\equiv (0,\\; -\\;\\frac{C}{B})$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$N \\equiv (\\;-\\;\\frac{C}{A},\\; 0)$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"661\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/perpendicular-distance-between-point-and-line-.png\" alt=\"Perpendicular distance between point and line\" class=\"wp-image-34592\" title=\"Perpendicular distance between point and line\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/perpendicular-distance-between-point-and-line-.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/perpendicular-distance-between-point-and-line--281x300.png 281w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>To find: distance between point P and line l, which is defined by the length d or length(PQ)<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">As mentioned earlier, PQ is the height of the $\\Delta PMN$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The formula for the area of a triangle is given by<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of triangle $= \\frac{1}{2} \\times$base $\\times$ height<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of PMN $= \\frac{1}{2}\\times$ MN $\\times$ PQ<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow PQ =&nbsp; \\frac{Area\\; of\\; \\Delta PMN \\times 2}{AB}$&nbsp; &#8212;&#8212;&#8212;&#8212; (i)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s find these two values on the R.H.S.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">According to coordinate geometry, the area of PMN can be given as&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Area of \\Delta PMN =&nbsp;\\frac{1}{2} |x\u2081(y\u2082\\;-\\;y\u2083) + x\u2082(y\u2083\\;-\\;y\u2081) + x\u2083( y\u2081\\;-\\;y\u2082)|$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= \\frac{1}{2} |x\u2081(0\\;-\\;(\\;-\\;\\frac{C}{B})) + (\\;-\\;\\frac{C}{A})((\\;-\\;\\frac{C}{B})\\;-\\;y\u2081) +0( y\u2081\\;-\\; 0)$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= \\frac{1}{2} | \\frac{x\u2081C}{B} +(\\frac{-C}{A})(\\frac{-C \\;-\\; By\u2081}{B})|$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= \\frac{1}{2} | \\frac{x\u2081C}{B} + (\\frac{C\u00b2}{AB} + \\frac{BCy\u2081}{AB})|$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= \\frac{1}{2} |\\frac{x\u2081C}{B}  + \\frac{Cy\u2081}{A} + \\frac{C\u00b2A}{B})|$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= \\frac{1}{2}| C(\\frac{x\u2081}{B} + \\frac{y\u2081}{A} + \\frac{C}{AB})|$ &#8212;&#8212;&#8212;&#8212;- (ii)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Multiple and divide the equation (ii) by AB&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Area\\; of\\; \\Delta PMN = \\frac{1}{2} |C(\\frac{ABx\u2081}{AB\u00b2} + \\frac{ABy\u2081}{A\u00b2B} + \\frac{ABC}{A\u00b2B\u00b2})|$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= \\frac{1}{2} |\\frac{CAx\u2081}{AB} + \\frac{CBy\u2081}{AB} + \\frac{C\u00b2}{AB})|$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= \\frac{1}{2} |\\frac{C}{AB}| (Ax\u2081 +  By\u2081 + C)$ &#8212;&#8212;&#8212;&#8212;&#8211; (iii)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Next, the distance of the line AB with coordinates $M(x\u2081,\\; y\u2081)$ and $N(x\u2082,\\; y\u2082)$ can be given by distance formula as&nbsp; $MN = \\sqrt{((x\u2082 \\;-\\; x\u2081)\u00b2+ (y\u2082 \\;-\\;y\u2081)\u00b2)}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In our case, $M(x\u2081,\\; y\u2081) = (0,\\; -\\;\\frac{C}{B})$ and $N(x\u2082,\\; y\u2082) = (\\;-\\;\\frac{C}{A},\\; 0)$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$MN = \\sqrt{((\\;-\\;\\frac{C}{A}) \\;-\\; 0)\u00b2 + (0 \\;-\\; (\\;-\\;CB))\u00b2)}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$MN = \\sqrt{(\\;-\\;CA)\u00b2 + (CB)\u00b2)}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$MN = |\\frac{C}{AB}| (A\u00b2 + B\u00b2 )$ &#8212;&#8212;&#8212;&#8212;- (iv)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Substituting equations (ii) and (iv) in equation (i)&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$PQ = \\frac{1}{2} \\times \\frac{|\\frac{CA}{B}| (Ax\u2081 + By\u2081 + C)&nbsp;\\times 2}{|\\frac{C}{AB}| (\\sqrt{A\u00b2+ B\u00b2})$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$PQ = d = \\frac{|(Ax\u2081 + By\u2081 + C)|}{\\sqrt{A\u00b2 + B\u00b2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Hence, we get that the distance between a point $(x\u2081,\\; y\u2081)$ and a line $Ax + By + C = 0$ is given&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$d = \\frac{|(Ax\u2081 + By\u2081 + C)|}{\\sqrt{A\u00b2 + B\u00b2}}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-facts-about-the-distance-between-point-and-line\">Facts about the Distance between Point and Line<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The distance between a point and a line can never be negative.&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The formula for distance <strong>between point and line <\/strong>has many practical applications in map navigation, construction, and sports.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The distance between origin and a line $Ax + By + C = 0$ is $d = \\frac{|C|}{\\sqrt{A\u00b2 + B\u00b2}}$.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The <strong>distance between point and line <\/strong>is a basic yet essential concept in coordinate geometry. We learned about the formula for finding the distance between a point and a line along with its derivation. Let\u2019s solve a few examples.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-solved-examples-on-distance-between-point-and-line\">Solved Examples on Distance between Point and Line<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 1: Find the distance between the point (0, 0) and the line <\/strong>$4x \\;-\\; 3y + 25 = 0$<strong>.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We have $P(x\u2081,\\; y\u2081) = (0, 0)$ and the line $4x \\;-\\; 3y + 25 = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x\u2081 = 0$ and $y\u2081&nbsp; = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$A = 4,\\; B = \\;-\\;3,\\; C = 25$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Using the formula for <strong>distance between point and line,<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$d = \\frac{|(Ax\u2081 + By\u2081 + C)|}{\\sqrt{A\u00b2 + B\u00b2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$d = \\frac{(4 \\times 0) + (\\;-\\;3 \\times 0)+ 25|}{sqrt{4\u00b2 + (\\;-\\;3)\u00b2}}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$d = \\frac{|0 + 0 + 25|}{\\sqrt{16 + 9}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$d = \\frac{25}{\\sqrt{16 + 9}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$d = \\frac{25}{\\sqrt{25}}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$d = \\frac{25}{5}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$d = 5$ units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 2: Find the distance between the point <\/strong>$(4,\\; 6)$<strong> and line <\/strong>$y = \\frac{1}{3}x \\;-\\; 3$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$(4,\\; 6) = (x\u2081,\\; y\u2081)$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x<sub>1<\/sub> = 4,\\; y<sub>1<\/sub> = 6$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$y = \\frac{1}{3}x \\;-\\; 3$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Add 3 on both sides of the equation.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$y + 3 = \\frac{1}{3}x \\;-\\; 3 + 3$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$y + 3 = \\frac{1}{3}x$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{1}{3}x \\;-\\; y + 3 = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Multiply both sides of the equation by 3<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x \\;-\\; 3y + 9 = 0$ &#8212;&#8212;&#8212;- (i)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Comparing equation (i) with $Ax + By + C = 0$, we get<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$A = 1,\\; B = \\;-\\;3,\\; C = 9$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Using the formula for distance between point and line&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$d = \\frac{|(Ax\u2081 + By\u2081 + C)|}{\\sqrt{A\u00b2 +  B\u00b2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$d = \\frac{|(1 \\times4) + (\\;-\\;3 \\times 6) + 9|}{\\sqrt{(\\;-\\;1)\u00b2 + (3)\u00b2}}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$d = \\frac{|4 \\;-\\; 18 + 9|}{1 + 9}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$d = \\frac{|\\;-\\;18 + 13|}{\\sqrt{10}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$d = \\frac{5}{\\sqrt{10}}$&nbsp; &nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$d = \\frac{5}{\\sqrt{10}}$&nbsp; units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 3: Find the distance between point P(6, 9) and line <\/strong>$2x \\;-\\; 5y + 7 = 0$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$P(6,\\; 9): x1 = 6,\\; y1 = 9$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Comparing equation (i) with $Ax + By + C = 0$, we get<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$A = 2,\\; B = \\;-\\;5, C = 7$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Using the formula for distance between point and line&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$d = \\frac{|(Ax\u2081 + By\u2081 + C)|}{\\sqrt{A\u00b2 + B\u00b2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$d = \\frac{|(2 \\times 6) + (- 5 \\times 9) + 7|}{\\sqrt{(2)\u00b2 + (\\;-\\;5)\u00b2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$d = \\frac{|12 &#8211; 45 + 7|}{\\sqrt{4 + 25}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$d = \\frac{|\\;-\\;45 + 19|}{\\sqrt{29}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$d = \\frac{|\\;-\\;26|}{\\sqrt{29}}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$d = \\frac{26}{\\sqrt{29}}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$d = \\frac{26}{\\sqrt{29}}$&nbsp; units<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-practice-problems-on-distance-between-point-and-line\">Practice Problems on Distance Between Point and Line<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Distance between Point and Line: Formula, Definition, Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Find the distance between the point (0, 7) and line $3x + 2y \\;-\\; 4 = 0$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{9}{\\sqrt{17}}$   units<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{18}{5}$ units<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{10}{\\sqrt{13}}$  units<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{18}{\\sqrt{13}}$   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: $\\frac{10}{\\sqrt{13}}$  units<br\/>$A = 3,\\; B = 2,\\; C = \\;-\\;4; (x\u2081,\\; y\u2081) = (0,\\; 7)$<br>\r\n$d = \\frac{|(Ax\u2081+ By\u2081+C)|}{\\sqrt{A\u00b2 + B\u00b2}} = \\frac{|(3(0)+ 2(7) \\;-\\;4)|}{\\sqrt{3\u00b2 + 2\u00b2}}  = \\frac{10}{\\sqrt{13}}$   <\/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\">What is the formula for finding the distance between a point$ (x\u2081, y\u2081)$ and a line $Ax + By + C = 0$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$d = \\frac{|(Ax\u2081 + By\u2081 + C)|}{\\sqrt{A\u00b2 + B\u00b2}}$  <\/div><div class=\"spq_answer_block\" data-value=\"1\">$d = \\frac{|(Ax\u2081 + By\u2081)|}{\\sqrt{A\u00b2 + B\u00b2}}$  <\/div><div class=\"spq_answer_block\" data-value=\"2\">$d = \\frac{|(Ax\u2081 + By\u2081 + C)|}{\\sqrt{A\u00b2\\;-\\; B\u00b2}}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$d = |(Ax\u2081 + By\u2081)|{\\sqrt{A\u00b2 + B\u00b2}}$<\/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: $d = \\frac{|(Ax\u2081 + By\u2081 + C)|}{\\sqrt{A\u00b2 + B\u00b2}}$  <br\/>The formula for finding the distance between a point $(x\u2081,\\; y\u2081)$ and a line $Ax + By + C = 0$ is<br> $d= \\frac{|(Ax\u2081 + By\u2081 + C)|}{\\sqrt{A\u00b2 + B\u00b2}}$ <\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">The distance of the point (0, 1) from x-axis is<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\sqrt{2}$  units<\/div><div class=\"spq_answer_block\" data-value=\"1\">1 unit<\/div><div class=\"spq_answer_block\" data-value=\"2\">2<\/div><div class=\"spq_answer_block\" data-value=\"3\">1.1 unit<\/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: 1 unit<br\/>Equation of x-axis: $y = 0$<br>\r\nComparing with $Ax + By + C = 0$, we get $A = 0,\\; B = 1,\\; C = 0$<br>\r\nPoint $= (0,\\; 1)$<br>\r\nThus, $d =  \\frac{|0 + (1)(1) + 0|}{\\sqrt{0 + 1}}   = 1$ unit<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">What is the distance of the point (1, 0) from the line $x = 1$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">1 unit<\/div><div class=\"spq_answer_block\" data-value=\"1\">2 unit<\/div><div class=\"spq_answer_block\" data-value=\"2\">0 unit<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\sqrt{2}$ unit<\/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: 0 unit<br\/>The point (1, 0) lies on the line  $x = 1$ since it satisfies the equation.<br>\r\nThus, the distance between $(1,\\; 0)$ and the line $x = 1$ is 0.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Distance between Point and Line: Formula, Definition, Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Distance between Point and Line\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the distance between the point (0, 7) and line $$3x + 2y \\\\;-\\\\; 4 = 0$$.\",\n                    \"text\": \"Find the distance between the point (0, 7) and line $$3x + 2y \\\\;-\\\\; 4 = 0$$.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$A = 3,\\\\; B = 2,\\\\; C = \\\\;-\\\\;4; (x\u2081,\\\\; y\u2081) = (0,\\\\; 7)$$<br>\r\n$$d = \\\\frac{|(Ax\u2081+ By\u2081+C)|}{\\\\sqrt{A\u00b2 + B\u00b2}} = \\\\frac{|(3(0)+ 2(7) \\\\;-\\\\;4)|}{\\\\sqrt{3\u00b2 + 2\u00b2}}  = \\\\frac{10}{\\\\sqrt{13}}$$   \"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{9}{\\\\sqrt{17}}$$   units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$A = 3,\\\\; B = 2,\\\\; C = \\\\;-\\\\;4; (x\u2081,\\\\; y\u2081) = (0,\\\\; 7)$$<br>\r\n$$d = \\\\frac{|(Ax\u2081+ By\u2081+C)|}{\\\\sqrt{A\u00b2 + B\u00b2}} = \\\\frac{|(3(0)+ 2(7) \\\\;-\\\\;4)|}{\\\\sqrt{3\u00b2 + 2\u00b2}}  = \\\\frac{10}{\\\\sqrt{13}}$$   \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{18}{5}$$ units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$A = 3,\\\\; B = 2,\\\\; C = \\\\;-\\\\;4; (x\u2081,\\\\; y\u2081) = (0,\\\\; 7)$$<br>\r\n$$d = \\\\frac{|(Ax\u2081+ By\u2081+C)|}{\\\\sqrt{A\u00b2 + B\u00b2}} = \\\\frac{|(3(0)+ 2(7) \\\\;-\\\\;4)|}{\\\\sqrt{3\u00b2 + 2\u00b2}}  = \\\\frac{10}{\\\\sqrt{13}}$$   \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{18}{\\\\sqrt{13}}$$   units \",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$A = 3,\\\\; B = 2,\\\\; C = \\\\;-\\\\;4; (x\u2081,\\\\; y\u2081) = (0,\\\\; 7)$$<br>\r\n$$d = \\\\frac{|(Ax\u2081+ By\u2081+C)|}{\\\\sqrt{A\u00b2 + B\u00b2}} = \\\\frac{|(3(0)+ 2(7) \\\\;-\\\\;4)|}{\\\\sqrt{3\u00b2 + 2\u00b2}}  = \\\\frac{10}{\\\\sqrt{13}}$$   \"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{10}{\\\\sqrt{13}}$$  units\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$A = 3,\\\\; B = 2,\\\\; C = \\\\;-\\\\;4; (x\u2081,\\\\; y\u2081) = (0,\\\\; 7)$$<br>\r\n$$d = \\\\frac{|(Ax\u2081+ By\u2081+C)|}{\\\\sqrt{A\u00b2 + B\u00b2}} = \\\\frac{|(3(0)+ 2(7) \\\\;-\\\\;4)|}{\\\\sqrt{3\u00b2 + 2\u00b2}}  = \\\\frac{10}{\\\\sqrt{13}}$$   \"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$A = 3,\\\\; B = 2,\\\\; C = \\\\;-\\\\;4; (x\u2081,\\\\; y\u2081) = (0,\\\\; 7)$$<br>\r\n$$d = \\\\frac{|(Ax\u2081+ By\u2081+C)|}{\\\\sqrt{A\u00b2 + B\u00b2}} = \\\\frac{|(3(0)+ 2(7) \\\\;-\\\\;4)|}{\\\\sqrt{3\u00b2 + 2\u00b2}}  = \\\\frac{10}{\\\\sqrt{13}}$$   \"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the formula for finding the distance between a point$$ (x\u2081, y\u2081)$$ and a line $$Ax + By + C = 0$$?\",\n                    \"text\": \"What is the formula for finding the distance between a point$$ (x\u2081, y\u2081)$$ and a line $$Ax + By + C = 0$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The formula for finding the distance between a point $$(x\u2081,\\\\; y\u2081)$$ and a line $$Ax + By + C = 0$$ is<br> $$d= \\\\frac{|(Ax\u2081 + By\u2081 + C)|}{\\\\sqrt{A\u00b2 + B\u00b2}}$$ \"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$d = \\\\frac{|(Ax\u2081 + By\u2081)|}{\\\\sqrt{A\u00b2 + B\u00b2}}$$  \",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The formula for finding the distance between a point $$(x\u2081,\\\\; y\u2081)$$ and a line $$Ax + By + C = 0$$ is<br> $$d= \\\\frac{|(Ax\u2081 + By\u2081 + C)|}{\\\\sqrt{A\u00b2 + B\u00b2}}$$ \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$d = \\\\frac{|(Ax\u2081 + By\u2081 + C)|}{\\\\sqrt{A\u00b2\\\\;-\\\\; B\u00b2}}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The formula for finding the distance between a point $$(x\u2081,\\\\; y\u2081)$$ and a line $$Ax + By + C = 0$$ is<br> $$d= \\\\frac{|(Ax\u2081 + By\u2081 + C)|}{\\\\sqrt{A\u00b2 + B\u00b2}}$$ \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$d = |(Ax\u2081 + By\u2081)|{\\\\sqrt{A\u00b2 + B\u00b2}}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The formula for finding the distance between a point $$(x\u2081,\\\\; y\u2081)$$ and a line $$Ax + By + C = 0$$ is<br> $$d= \\\\frac{|(Ax\u2081 + By\u2081 + C)|}{\\\\sqrt{A\u00b2 + B\u00b2}}$$ \"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$d = \\\\frac{|(Ax\u2081 + By\u2081 + C)|}{\\\\sqrt{A\u00b2 + B\u00b2}}$$  \",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The formula for finding the distance between a point $$(x\u2081,\\\\; y\u2081)$$ and a line $$Ax + By + C = 0$$ is<br> $$d= \\\\frac{|(Ax\u2081 + By\u2081 + C)|}{\\\\sqrt{A\u00b2 + B\u00b2}}$$ \"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The formula for finding the distance between a point $$(x\u2081,\\\\; y\u2081)$$ and a line $$Ax + By + C = 0$$ is<br> $$d= \\\\frac{|(Ax\u2081 + By\u2081 + C)|}{\\\\sqrt{A\u00b2 + B\u00b2}}$$ \"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The distance of the point (0, 1) from x-axis is\",\n                    \"text\": \"The distance of the point (0, 1) from x-axis is\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Equation of x-axis: $$y = 0$$<br>\r\nComparing with $$Ax + By + C = 0$$, we get $$A = 0,\\\\; B = 1,\\\\; C = 0$$<br>\r\nPoint $$= (0,\\\\; 1)$$<br>\r\nThus, $$d =  \\\\frac{|0 + (1)(1) + 0|}{\\\\sqrt{0 + 1}}   = 1$$ unit\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\sqrt{2}$$  units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Equation of x-axis: $$y = 0$$<br>\r\nComparing with $$Ax + By + C = 0$$, we get $$A = 0,\\\\; B = 1,\\\\; C = 0$$<br>\r\nPoint $$= (0,\\\\; 1)$$<br>\r\nThus, $$d =  \\\\frac{|0 + (1)(1) + 0|}{\\\\sqrt{0 + 1}}   = 1$$ unit\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Equation of x-axis: $$y = 0$$<br>\r\nComparing with $$Ax + By + C = 0$$, we get $$A = 0,\\\\; B = 1,\\\\; C = 0$$<br>\r\nPoint $$= (0,\\\\; 1)$$<br>\r\nThus, $$d =  \\\\frac{|0 + (1)(1) + 0|}{\\\\sqrt{0 + 1}}   = 1$$ unit\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1.1 unit\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Equation of x-axis: $$y = 0$$<br>\r\nComparing with $$Ax + By + C = 0$$, we get $$A = 0,\\\\; B = 1,\\\\; C = 0$$<br>\r\nPoint $$= (0,\\\\; 1)$$<br>\r\nThus, $$d =  \\\\frac{|0 + (1)(1) + 0|}{\\\\sqrt{0 + 1}}   = 1$$ unit\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"1 unit\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Equation of x-axis: $$y = 0$$<br>\r\nComparing with $$Ax + By + C = 0$$, we get $$A = 0,\\\\; B = 1,\\\\; C = 0$$<br>\r\nPoint $$= (0,\\\\; 1)$$<br>\r\nThus, $$d =  \\\\frac{|0 + (1)(1) + 0|}{\\\\sqrt{0 + 1}}   = 1$$ unit\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Equation of x-axis: $$y = 0$$<br>\r\nComparing with $$Ax + By + C = 0$$, we get $$A = 0,\\\\; B = 1,\\\\; C = 0$$<br>\r\nPoint $$= (0,\\\\; 1)$$<br>\r\nThus, $$d =  \\\\frac{|0 + (1)(1) + 0|}{\\\\sqrt{0 + 1}}   = 1$$ unit\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the distance of the point (1, 0) from the line $$x = 1$$?\",\n                    \"text\": \"What is the distance of the point (1, 0) from the line $$x = 1$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The point (1, 0) lies on the line  $$x = 1$$ since it satisfies the equation.<br>\r\nThus, the distance between $$(1,\\\\; 0)$$ and the line $$x = 1$$ is 0.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1 unit\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The point (1, 0) lies on the line  $$x = 1$$ since it satisfies the equation.<br>\r\nThus, the distance between $$(1,\\\\; 0)$$ and the line $$x = 1$$ is 0.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2 unit\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The point (1, 0) lies on the line  $$x = 1$$ since it satisfies the equation.<br>\r\nThus, the distance between $$(1,\\\\; 0)$$ and the line $$x = 1$$ is 0.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\sqrt{2}$$ unit\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The point (1, 0) lies on the line  $$x = 1$$ since it satisfies the equation.<br>\r\nThus, the distance between $$(1,\\\\; 0)$$ and the line $$x = 1$$ is 0.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"0 unit\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The point (1, 0) lies on the line  $$x = 1$$ since it satisfies the equation.<br>\r\nThus, the distance between $$(1,\\\\; 0)$$ and the line $$x = 1$$ is 0.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The point (1, 0) lies on the line  $$x = 1$$ since it satisfies the equation.<br>\r\nThus, the distance between $$(1,\\\\; 0)$$ and the line $$x = 1$$ is 0.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-frequently-asked-questions-on-the-distance-between-point-and-line\">Frequently Asked Questions on the Distance between Point and Line<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-4ccd4f1a-44dd-4ebc-9839-53006c7bcc6f\" 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-0-4ccd4f1a-44dd-4ebc-9839-53006c7bcc6f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-4ccd4f1a-44dd-4ebc-9839-53006c7bcc6f\"><strong>What is the shortest distance between a point and a line?<\/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-0-4ccd4f1a-44dd-4ebc-9839-53006c7bcc6f\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">It is the length of a perpendicular drawn from the point to the line.<\/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-1-4ccd4f1a-44dd-4ebc-9839-53006c7bcc6f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-4ccd4f1a-44dd-4ebc-9839-53006c7bcc6f\"><strong>What is 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-1-4ccd4f1a-44dd-4ebc-9839-53006c7bcc6f\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The distance between two points is the length of the line segment that connects them on a plane. The formula is $d = ((x_2 \\;-\\; x_1)^2 + (y_2 \\;-\\;y_1)^2)$ , where $(x_1,\\; y_1)$ and $(x_2,\\; y_2)$ are the coordinates of the two 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-2-4ccd4f1a-44dd-4ebc-9839-53006c7bcc6f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-4ccd4f1a-44dd-4ebc-9839-53006c7bcc6f\"><strong>What is the equation for a straight line in the slop-intercept form?<\/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-2-4ccd4f1a-44dd-4ebc-9839-53006c7bcc6f\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The equation for a straight line in the slope point form is given by $y = mx + c$, where m is the slope and c is the y-intercept.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Distance between a Point and a Line? The distance between point and line is the shortest distance between the point and the straight line.&nbsp; Consider a line BF and a point A as shown in the diagram below. We can draw an infinite number of line segments from the line to the &#8230; <a title=\"Distance between Point and Line: Formula, Definition, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/distance-of-a-point-from-a-line\" aria-label=\"More on Distance between Point and Line: Formula, Definition, Examples\">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-29364","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\/29364","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=29364"}],"version-history":[{"count":11,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/29364\/revisions"}],"predecessor-version":[{"id":34593,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/29364\/revisions\/34593"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=29364"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=29364"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=29364"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}