If a line has a slope of 3\/4, what is the slope of the line perpendicular to the line?<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n The slope of the line perpendicular to a line with a slope of ( \\frac{3}{4} ) is ( -\\frac{4}{3} ).<\/p>\n\n\n\n In geometry, the slope of a line represents how steep the line is. Slope is often denoted by the letter ( m ) and is calculated as the “rise over run,” or the change in ( y )-coordinates divided by the change in ( x )-coordinates between two points on the line.<\/p>\n\n\n\n For two lines to be perpendicular, their slopes must be negative reciprocals<\/strong> of each other. This means that when you multiply the slopes of two perpendicular lines, the result should be ( -1 ). Mathematically, if the slope of one line is ( m_1 ), and the slope of the perpendicular line is ( m_2 ), then the relationship is:<\/p>\n\n\n\n [ In this problem, the slope of the first line, ( m_1 ), is ( \\frac{3}{4} ). To find the slope of the line perpendicular to it, ( m_2 ), we use the negative reciprocal of ( \\frac{3}{4} ). The reciprocal of ( \\frac{3}{4} ) is ( \\frac{4}{3} ), and the negative reciprocal would be ( -\\frac{4}{3} ).<\/p>\n\n\n\n To verify this, let\u2019s multiply the two slopes:<\/p>\n\n\n\n [ Since the product of the slopes is ( -1 ), the lines are indeed perpendicular.<\/p>\n\n\n\n In summary, the slope of a line perpendicular to one with a slope of ( \\frac{3}{4} ) is ( -\\frac{4}{3} ). This concept is useful in coordinate geometry when determining relationships between lines, particularly in problems involving right angles, constructing perpendicular bisectors, or analyzing geometric shapes.<\/p>\n","protected":false},"excerpt":{"rendered":" If a line has a slope of 3\/4, what is the slope of the line perpendicular to the line? The Correct Answer and Explanation is: The slope of the line perpendicular to a line with a slope of ( \\frac{3}{4} ) is ( -\\frac{4}{3} ). Explanation: In geometry, the slope of a line represents how […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-154820","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/154820","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=154820"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/154820\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=154820"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=154820"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=154820"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Explanation:<\/h3>\n\n\n\n
m_1 \\times m_2 = -1
]<\/p>\n\n\n\n
\\frac{3}{4} \\times -\\frac{4}{3} = -\\frac{12}{12} = -1
]<\/p>\n\n\n\n