{"id":35068,"date":"2023-10-18T06:39:18","date_gmt":"2023-10-18T06:39:18","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=35068"},"modified":"2023-10-18T11:53:45","modified_gmt":"2023-10-18T11:53:45","slug":"slope-of-perpendicular-lines-definition-formula-examples-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/slope-of-perpendicular-lines","title":{"rendered":"Slope of Perpendicular Lines &#8211; Definition, Formula, Examples, FAQs"},"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-61748814-9285-400d-b33b-129605bc7564\" 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\/slope-of-perpendicular-lines#0-what-is-the-slope-of-perpendicular-lines>What Is the Slope of Perpendicular Lines?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/slope-of-perpendicular-lines#1-formula-for-finding-the-slope-of-perpendicular-lines>Formula for Finding the Slope of Perpendicular Lines<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/slope-of-perpendicular-lines#3-how-to-find-the-slope-of-a-line-perpendicular-to-the-given-line>How to Find the Slope of a Line Perpendicular to the Given Line<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/slope-of-perpendicular-lines#8-solved-examples-on-slope-of-perpendicular-lines>Solved Examples on Slope of Perpendicular Lines<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/slope-of-perpendicular-lines#9-practice-problems-on-slope-of-perpendicular-lines>Practice Problems on Slope of Perpendicular Lines<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/slope-of-perpendicular-lines#10-frequently-asked-questions-about-slope-of-perpendicular-lines>Frequently Asked Questions about Slope of Perpendicular Lines<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-the-slope-of-perpendicular-lines\">What Is the Slope of Perpendicular Lines?<\/h2>\n\n\n\n<p><strong>The slopes of two perpendicular lines are negative reciprocals of each other. In simple words, the product of the slopes of two perpendicular lines equals <\/strong><strong>-1<\/strong><strong>.<\/strong><\/p>\n\n\n\n<p>Two <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/line\">lines<\/a> are said to be <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/perpendicular\">perpendicular<\/a> if they intersect each other at a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/right-angle\">right angle<\/a> (90).&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"661\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/perpendicular-lines.png\" alt=\"Perpendicular lines\" class=\"wp-image-35070\" title=\"Perpendicular lines\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/perpendicular-lines.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/perpendicular-lines-281x300.png 281w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\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-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\/divide-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\/mult_div_facts_divide_nl_pt.png\" alt=\"Divide 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\">Divide 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\/identify-fractions-on-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_identify_fraction_nl_pt.png\" alt=\"Identify Fractions on 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\">Identify Fractions on 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\/identify-lines-line-segments-rays-angles\" 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\/geometry_identify_pt_line_ray_angle_pt.png\" alt=\"Identify Lines, Line Segments, Rays, Angles 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\">Identify Lines, Line Segments, Rays, Angles 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\/identify-parallel-and-perpendicular-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\/geometry_identify_types_of_lines_pt.png\" alt=\"Identify Parallel and Perpendicular 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\">Identify Parallel and Perpendicular 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\/identify-the-lines-of-symmetry-in-irregular-shapes\" 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\/geometry_symm_irregular_shape_pt.png\" alt=\"Identify the LInes of Symmetry in Irregular Shapes 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\">Identify the LInes of Symmetry in Irregular Shapes 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\/identify-the-lines-of-symmetry-in-quadrilaterals\" 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\/geometry_symm_regular_shape_pt.png\" alt=\"Identify the LInes of Symmetry in Quadrilaterals 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\">Identify the LInes of Symmetry in Quadrilaterals 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\/mark-fractions-on-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_place_fraction_nl_pt.png\" alt=\"Mark Fractions on 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\">Mark Fractions on 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\/mark-unit-fractions-on-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_place_unit_fraction_nl_pt.png\" alt=\"Mark Unit Fractions on 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\">Mark Unit Fractions on 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\/missing-denominators-on-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_missing_deno_nl_pt.png\" alt=\"Missing Denominators on 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\">Missing Denominators on 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><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                    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         }\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\" id=\"1-formula-for-finding-the-slope-of-perpendicular-lines\">Formula for Finding the Slope of Perpendicular Lines<\/h2>\n\n\n\n<p>If the slopes of the two perpendicular lines are m<sub>1<\/sub> and m<sub>2<\/sub>, then the relationship between the slopes is given by the formula&nbsp;<\/p>\n\n\n\n<p>$m_{1} \\times m_{2} = -1$\u00a0<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"832\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/slopes-of-perpendicular-lines.png\" alt=\"Slopes of perpendicular lines\" class=\"wp-image-35075\" title=\"Slopes of perpendicular lines\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/slopes-of-perpendicular-lines.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/slopes-of-perpendicular-lines-224x300.png 224w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"2-slope-of-perpendicular-lines-negative-reciprocals\">Slope of Perpendicular Lines: Negative Reciprocals<\/h2>\n\n\n\n<p>The slopes of perpendicular lines are negative reciprocals of each other. Thus, the slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line.<\/p>\n\n\n\n<p>A reciprocal is defined as the multiplicative inverse of a given number. The <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/multiplicative-inverse\">multiplicative inverse<\/a> (or <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/reciprocal\">reciprocal<\/a>) of a non-zero number \u201ca\u201d is written as $\\frac{1}{a}$.\u00a0<\/p>\n\n\n\n<p>To obtain the negative reciprocal of a particular value, just add a minus sign to its reciprocal. So, the negative reciprocal of \u201ca\u201d can be written as $\\frac{-1}{a}$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"341\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/how-to-find-negative-reciprocals.png\" alt=\"How to find negative reciprocals\" class=\"wp-image-35077\" title=\"How to find negative reciprocals\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/how-to-find-negative-reciprocals.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/how-to-find-negative-reciprocals-300x165.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-how-to-find-the-slope-of-a-line-perpendicular-to-the-given-line\">How to Find the Slope of a Line Perpendicular to the Given Line<\/h2>\n\n\n\n<p>If the slope of one line is known, the slope of the line perpendicular to it is calculated as the negative reciprocal of the first line.<\/p>\n\n\n\n<p>The general form of the equation of a line is given as<\/p>\n\n\n\n<p>$ax + by + c = 0$<\/p>\n\n\n\n<p>Convert this equation into the slope-intercept form of the equation of a line.<\/p>\n\n\n\n<p>$y = \\frac{-ax}{b} \\;-\\; \\frac{c}{b}$<\/p>\n\n\n\n<p>So, we get the slope for the line would be&nbsp;<\/p>\n\n\n\n<p>$m_{1} = -\\;\\frac{a}{b}$<\/p>\n\n\n\n<p>The general formula for the slope of perpendicular lines is&nbsp;<\/p>\n\n\n\n<p>$m_{1} . m_{2} = -1$<\/p>\n\n\n\n<p>$\\Rightarrow -\\;\\frac{a}{b} . m_{2} = -\\;1$<\/p>\n\n\n\n<p>$\\Rightarrow m_{2} = \\frac{b}{a}$<\/p>\n\n\n\n<p>Therefore, the slope of the perpendicular line would be $\\frac{b}{a}$.<\/p>\n\n\n\n<p><strong>Example<\/strong>: Find the slope of a line perpendicular to the line $y = -\\;2x + 1$.<\/p>\n\n\n\n<p>Given line: $y = -\\;2x + 1$.<\/p>\n\n\n\n<p>Slope of the given line $= m = -\\;2$<\/p>\n\n\n\n<p>Slopes of perpendicular lines are negative reciprocals of each other.<\/p>\n\n\n\n<p>Thus, slope of the line perpendicular to the given line is $-\\;\\frac{1}{-\\;2} = \\frac{1}{2}$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-derivation-of-the-formula-for-finding-the-slope-of-perpendicular-lines\">Derivation of the Formula for Finding the Slope of Perpendicular Lines<\/h2>\n\n\n\n<p>The <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/angle\">angle<\/a> between the two lines with slopes m<sub>1<\/sub> and m<sub>2<\/sub> is obtained using the formula<\/p>\n\n\n\n<p>tan $\\theta = \\frac{m_{1}-m_{2}}{1 + m_{1} m_{2}}$<\/p>\n\n\n\n<p>If two lines are perpendicular, then $\\theta = 90^{\\circ}$.<\/p>\n\n\n\n<p>tan $90^{\\circ} = \\frac{m_{1}-m_{2}}{1 + m_{1}m_{2}}$<\/p>\n\n\n\n<p>Note that tan $90^{\\circ}$ is not defined.<\/p>\n\n\n\n<p>$\\infty = \\frac{m_{1}-m_{2}}{1 + m_{1}m_{2}}$<\/p>\n\n\n\n<p>Thus, $1 + m_{1} m_{2} = 0$<\/p>\n\n\n\n<p>$m_{1} m_{2} = -1$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-what-is-the-slope-of-parallel-lines-and-perpendicular-lines\">What Is the Slope of Parallel Lines and Perpendicular Lines?<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If two lines are parallel, they have the same slope. In other words, the slopes of two parallel lines are equal.<\/li>\n<\/ul>\n\n\n\n<p>If lines l and m are parallel, such that the slope of line l is m1 and the slope of line m is m2, then&nbsp;<\/p>\n\n\n\n<p>$m_{1} = m_{2}$.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>On the other hand, the slopes of two perpendicular lines are negative reciprocals of each other.<\/li>\n<\/ul>\n\n\n\n<p>If lines l and m are perpendicular, such that the slope of line l is m1 and the slope of line m is m2, then&nbsp;<\/p>\n\n\n\n<p>$m_{1} m_{2} = -\\;1$\u00a0<\/p>\n\n\n\n<p>or&nbsp;<\/p>\n\n\n\n<p>$m_{1} = \\frac{-1}{m_{2}}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-facts-about-slope-of-perpendicular-lines\">Facts about Slope of Perpendicular Lines<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>Perpendicular lines form right angles at the point they intersect.<\/li>\n\n\n\n<li>If two lines are <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/parallel-lines\">parallel<\/a>, their slopes are equal.<\/li>\n\n\n\n<li>If the slope of a line is m, the slope of the line perpendicular to it is -1m.<\/li>\n\n\n\n<li>A <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/vertical\">vertical line<\/a> line is always perpendicular to a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/horizontal\">horizontal line<\/a>.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned how to find the slope of perpendicular lines, the associated formula, and its derivation. Let\u2019s solve a few examples and practice MCQs on these concepts for better comprehension.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-solved-examples-on-slope-of-perpendicular-lines\">Solved Examples on Slope of Perpendicular Lines<\/h2>\n\n\n\n<p><strong>Example 1: What will be the slope of the line\u00a0 perpendicular to the line <\/strong>$6x &#8211; 2y = 4$<strong>?<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Given line: $6x &#8211; 2y &#8211; 4 = 0$<\/p>\n\n\n\n<p>$6x &#8211; 2y = 4$<\/p>\n\n\n\n<p>$\\Rightarrow -\\; 2y = 4\\;-\\;6x$<\/p>\n\n\n\n<p>$\\Rightarrow y = 3x\\;-\\;2$<\/p>\n\n\n\n<p>Slope of the first line $= m_{1} = 3$<\/p>\n\n\n\n<p>Slope of the perpendicular line $= \\frac{-1}{m_{1}}$<\/p>\n\n\n\n<p>$\\Rightarrow m_{2} = -\\;\\frac{1}{3}$<\/p>\n\n\n\n<p>Therefore, the slope of the perpendicular line would be $-\\;\\frac{1}{3}$.<\/p>\n\n\n\n<p><strong>Example 2: What will be the equation of a line passing through the point (5, 2) and with the slope of the perpendicular line equal to <\/strong><strong>-3<\/strong><strong>?<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>The slope of the perpendicular line is $m_{1} = \\;-\\;3$.<\/p>\n\n\n\n<p>From the formula of the slope of the perpendicular lines<\/p>\n\n\n\n<p>$m_{1} .m_{2} = -1$<\/p>\n\n\n\n<p>$\\Rightarrow -\\;3 \\times m_{2} = -\\;1$<\/p>\n\n\n\n<p>$m_{2} = \\frac{1}{3}$<\/p>\n\n\n\n<p>The line passes through the point $(x_{1},\\; y_{1}) = (5,\\; 2)$ and has slope $m = \\frac{1}{3}$.<\/p>\n\n\n\n<p>To find the equation of the required line, we will use the slope-point form.&nbsp;<\/p>\n\n\n\n<p>$(y\\;-\\;y_{1}) = m(x\\;-\\;x_{1})$<\/p>\n\n\n\n<p>$\\Rightarrow (y\\;-\\;2) = \\frac{1}{3} (x \\;-\\;5)$\u00a0<\/p>\n\n\n\n<p>$\\Rightarrow 3(y\\;-\\;2) = 1(x\\;-\\;5)$<\/p>\n\n\n\n<p>$\\Rightarrow 3y\\;-\\;6 = x\\;-\\;5$<\/p>\n\n\n\n<p>$\\Rightarrow x\\;-\\;3y + 6\\;-\\;5 = 0$<\/p>\n\n\n\n<p>$\\Rightarrow x\\;-\\;3y +1 = 0$<\/p>\n\n\n\n<p>Therefore, the equation of the line is $x\\;-\\;3y + 1 = 0$.<\/p>\n\n\n\n<p><strong>Example 3: Find the slope of a line perpendicular to the line passing through points <\/strong><strong>(1, 2)<\/strong><strong> and <\/strong><strong>(3, 4)<\/strong><strong>.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Slope of a line passing through the points $(x_{1},\\;y_{1})$ and $(x_{2},\\;y_{2})$ is given by<\/p>\n\n\n\n<p>Slope $= \\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$<\/p>\n\n\n\n<p>Here, $(x_{1},\\;y_{1}) = (1,\\; 2)$<strong> <\/strong>and<strong> <\/strong>$(x_{2},\\;y_{2}) = (3,\\; 4)$<\/p>\n\n\n\n<p>Slope $= \\frac{4 &#8211; 2}{3 &#8211; 1}$<\/p>\n\n\n\n<p>$m = \\frac{2}{2} = 1$<\/p>\n\n\n\n<p>Slope of the required line $= \\frac{-1}{m} = -\\;1$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-practice-problems-on-slope-of-perpendicular-lines\">Practice Problems on Slope of Perpendicular Lines<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Slope of Perpendicular Lines - Definition, Formula, Examples, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">What is the slope of the line perpendicular to the line whose slope is $\\frac{6}{7}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{6}{7}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$-\\;\\frac{6}{7}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{7}{6}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$-\\;\\frac{7}{6}$<\/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: $-\\;\\frac{7}{6}$<br\/>$m_{1}.m_{2} = -\\;1$<br>\r\n$\\Rightarrow \\frac{6}{7} \\times m_{2} = -\\;1$<br>\r\n$\\Rightarrow m_{2} = -\\;\\frac{7}{6}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Find the slope of the line perpendicular to $3x \\;-\\;4y + 5 = 0$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{3}{4}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{-4}{3}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{4}{3}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{-3}{4}$<\/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: $\\frac{-4}{3}$<br\/>$3x \\;-\\;4y + 5 = 0 \\;m_{1} = -\\;\\frac{a}{b} \\Rightarrow m_{1} = -\\;\\frac{3}{-4} = \\frac{3}{4}$.<br>\r\n$\\Rightarrow m_{1} m_{2} = -\\;1$<br>\r\n$\\Rightarrow \\frac{3}{4} \\times m_{2} = -\\;1$<br>\r\n$\\Rightarrow m_{2} = -\\;\\frac{4}{3}$<\/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\">Slopes of perpendicular lines are<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">reciprocals<\/div><div class=\"spq_answer_block\" data-value=\"1\">multiplicative inverses<\/div><div class=\"spq_answer_block\" data-value=\"2\">additive inverses<\/div><div class=\"spq_answer_block\" data-value=\"3\">negative reciprocals<\/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: negative reciprocals<br\/>Slopes of perpendicular lines are negative reciprocals of each other.<\/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\">If the slopes of two perpendicular lines are m and n, then<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">m + n = 0<\/div><div class=\"spq_answer_block\" data-value=\"1\">mn = 1<\/div><div class=\"spq_answer_block\" data-value=\"2\">mn = -1<\/div><div class=\"spq_answer_block\" data-value=\"3\">m - n = 0<\/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: mn = -1<br\/>If the slopes of two perpendicular lines are m and n, then $mn = -\\;1$.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        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$$\\\\frac{6}{7}$$?\",\n                    \"text\": \"What is the slope of the line perpendicular to the line whose slope is $$\\\\frac{6}{7}$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$m_{1}.m_{2} = -\\\\;1$$<br>\r\n$$\\\\Rightarrow \\\\frac{6}{7} \\\\times m_{2} = -\\\\;1$$<br>\r\n$$\\\\Rightarrow m_{2} = -\\\\;\\\\frac{7}{6}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{6}{7}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$m_{1}.m_{2} = -\\\\;1$$<br>\r\n$$\\\\Rightarrow \\\\frac{6}{7} \\\\times m_{2} = -\\\\;1$$<br>\r\n$$\\\\Rightarrow m_{2} = -\\\\;\\\\frac{7}{6}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$-\\\\;\\\\frac{6}{7}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$m_{1}.m_{2} = -\\\\;1$$<br>\r\n$$\\\\Rightarrow \\\\frac{6}{7} \\\\times m_{2} = -\\\\;1$$<br>\r\n$$\\\\Rightarrow m_{2} = -\\\\;\\\\frac{7}{6}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{7}{6}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$m_{1}.m_{2} = -\\\\;1$$<br>\r\n$$\\\\Rightarrow \\\\frac{6}{7} \\\\times m_{2} = -\\\\;1$$<br>\r\n$$\\\\Rightarrow m_{2} = -\\\\;\\\\frac{7}{6}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$-\\\\;\\\\frac{7}{6}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$m_{1}.m_{2} = -\\\\;1$$<br>\r\n$$\\\\Rightarrow \\\\frac{6}{7} \\\\times m_{2} = -\\\\;1$$<br>\r\n$$\\\\Rightarrow m_{2} = -\\\\;\\\\frac{7}{6}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$m_{1}.m_{2} = -\\\\;1$$<br>\r\n$$\\\\Rightarrow \\\\frac{6}{7} \\\\times m_{2} = -\\\\;1$$<br>\r\n$$\\\\Rightarrow m_{2} = -\\\\;\\\\frac{7}{6}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the slope of the line perpendicular to $$3x \\\\;-\\\\;4y + 5 = 0$$.\",\n                    \"text\": \"Find the slope of the line perpendicular to $$3x \\\\;-\\\\;4y + 5 = 0$$.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$3x \\\\;-\\\\;4y + 5 = 0 \\\\;m_{1} = -\\\\;\\\\frac{a}{b} \\\\Rightarrow m_{1} = -\\\\;\\\\frac{3}{-4} = \\\\frac{3}{4}$$.<br>\r\n$$\\\\Rightarrow m_{1} m_{2} = -\\\\;1$$<br>\r\n$$\\\\Rightarrow \\\\frac{3}{4} \\\\times m_{2} = -\\\\;1$$<br>\r\n$$\\\\Rightarrow m_{2} = -\\\\;\\\\frac{4}{3}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{3}{4}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$3x \\\\;-\\\\;4y + 5 = 0 \\\\;m_{1} = -\\\\;\\\\frac{a}{b} \\\\Rightarrow m_{1} = -\\\\;\\\\frac{3}{-4} = \\\\frac{3}{4}$$.<br>\r\n$$\\\\Rightarrow m_{1} m_{2} = -\\\\;1$$<br>\r\n$$\\\\Rightarrow \\\\frac{3}{4} \\\\times m_{2} = -\\\\;1$$<br>\r\n$$\\\\Rightarrow m_{2} = -\\\\;\\\\frac{4}{3}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{4}{3}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$3x \\\\;-\\\\;4y + 5 = 0 \\\\;m_{1} = -\\\\;\\\\frac{a}{b} \\\\Rightarrow m_{1} = -\\\\;\\\\frac{3}{-4} = \\\\frac{3}{4}$$.<br>\r\n$$\\\\Rightarrow m_{1} m_{2} = -\\\\;1$$<br>\r\n$$\\\\Rightarrow \\\\frac{3}{4} \\\\times m_{2} = -\\\\;1$$<br>\r\n$$\\\\Rightarrow m_{2} = -\\\\;\\\\frac{4}{3}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{-3}{4}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$3x \\\\;-\\\\;4y + 5 = 0 \\\\;m_{1} = -\\\\;\\\\frac{a}{b} \\\\Rightarrow m_{1} = -\\\\;\\\\frac{3}{-4} = \\\\frac{3}{4}$$.<br>\r\n$$\\\\Rightarrow m_{1} m_{2} = -\\\\;1$$<br>\r\n$$\\\\Rightarrow \\\\frac{3}{4} \\\\times m_{2} = -\\\\;1$$<br>\r\n$$\\\\Rightarrow m_{2} = -\\\\;\\\\frac{4}{3}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{-4}{3}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$3x \\\\;-\\\\;4y + 5 = 0 \\\\;m_{1} = -\\\\;\\\\frac{a}{b} \\\\Rightarrow m_{1} = -\\\\;\\\\frac{3}{-4} = \\\\frac{3}{4}$$.<br>\r\n$$\\\\Rightarrow m_{1} m_{2} = -\\\\;1$$<br>\r\n$$\\\\Rightarrow \\\\frac{3}{4} \\\\times m_{2} = -\\\\;1$$<br>\r\n$$\\\\Rightarrow m_{2} = -\\\\;\\\\frac{4}{3}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$3x \\\\;-\\\\;4y + 5 = 0 \\\\;m_{1} = -\\\\;\\\\frac{a}{b} \\\\Rightarrow m_{1} = -\\\\;\\\\frac{3}{-4} = \\\\frac{3}{4}$$.<br>\r\n$$\\\\Rightarrow m_{1} m_{2} = -\\\\;1$$<br>\r\n$$\\\\Rightarrow \\\\frac{3}{4} \\\\times m_{2} = -\\\\;1$$<br>\r\n$$\\\\Rightarrow m_{2} = -\\\\;\\\\frac{4}{3}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Slopes of perpendicular lines are\",\n                    \"text\": \"Slopes of perpendicular lines are\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Slopes of perpendicular lines are negative reciprocals of each other.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"reciprocals\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Slopes of perpendicular lines are negative reciprocals of each other.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"multiplicative inverses\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Slopes of perpendicular lines are negative reciprocals of each other.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"additive inverses\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Slopes of perpendicular lines are negative reciprocals of each other.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"negative reciprocals\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Slopes of perpendicular lines are negative reciprocals of each other.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Slopes of perpendicular lines are negative reciprocals of each other.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If the slopes of two perpendicular lines are m and n, then\",\n                    \"text\": \"If the slopes of two perpendicular lines are m and n, then\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"If the slopes of two perpendicular lines are m and n, then $$mn = -\\\\;1$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"m + n = 0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If the slopes of two perpendicular lines are m and n, then $$mn = -\\\\;1$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"mn = 1\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If the slopes of two perpendicular lines are m and n, then $$mn = -\\\\;1$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"m - n = 0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If the slopes of two perpendicular lines are m and n, then $$mn = -\\\\;1$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"mn = -1\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"If the slopes of two perpendicular lines are m and n, then $$mn = -\\\\;1$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"If the slopes of two perpendicular lines are m and n, then $$mn = -\\\\;1$$.\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-frequently-asked-questions-about-slope-of-perpendicular-lines\">Frequently Asked Questions about Slope of Perpendicular Lines<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-a742e653-a8e7-4f82-ab0f-3bedc7b74ece\" 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-a742e653-a8e7-4f82-ab0f-3bedc7b74ece\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a742e653-a8e7-4f82-ab0f-3bedc7b74ece\"><strong>Do perpendicular lines have the same slope?<\/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-a742e653-a8e7-4f82-ab0f-3bedc7b74ece\">\n\n<p>Perpendicular lines do not have the same slope. The slopes of the perpendicular line are negative reciprocals of each other.<\/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-a742e653-a8e7-4f82-ab0f-3bedc7b74ece\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a742e653-a8e7-4f82-ab0f-3bedc7b74ece\"><strong>What is the slope of parallel lines?<\/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-a742e653-a8e7-4f82-ab0f-3bedc7b74ece\">\n\n<p>The slope of parallel lines is equal to each other. Any lines that are parallel to each other have the same slope but different y-intercepts.<\/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-a742e653-a8e7-4f82-ab0f-3bedc7b74ece\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a742e653-a8e7-4f82-ab0f-3bedc7b74ece\"><strong>How do you identify perpendicular lines from slopes?<\/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-a742e653-a8e7-4f82-ab0f-3bedc7b74ece\">\n\n<p>If the product of slopes is -1, the two lines are perpendicular.<\/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-a742e653-a8e7-4f82-ab0f-3bedc7b74ece\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a742e653-a8e7-4f82-ab0f-3bedc7b74ece\"><strong>How do you describe the slopes of perpendicular lines?<\/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-a742e653-a8e7-4f82-ab0f-3bedc7b74ece\">\n\n<p>The slopes of two perpendicular lines are negative reciprocals of each other. If the slope of a line is m, the slope of the line perpendicular to it is the negative reciprocal of m, given by $\\frac{-1}{m}$.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Slope of Perpendicular Lines? The slopes of two perpendicular lines are negative reciprocals of each other. In simple words, the product of the slopes of two perpendicular lines equals -1. Two lines are said to be perpendicular if they intersect each other at a right angle (90).&nbsp; Recommended Games Add Like Fractions &#8230; <a title=\"Slope of Perpendicular Lines &#8211; Definition, Formula, Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/slope-of-perpendicular-lines\" aria-label=\"More on Slope of Perpendicular Lines &#8211; Definition, Formula, Examples, FAQs\">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-35068","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\/35068","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=35068"}],"version-history":[{"count":8,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/35068\/revisions"}],"predecessor-version":[{"id":35086,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/35068\/revisions\/35086"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=35068"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=35068"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=35068"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}