{"id":227744,"date":"2025-06-06T12:27:47","date_gmt":"2025-06-06T12:27:47","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=227744"},"modified":"2025-06-06T12:27:50","modified_gmt":"2025-06-06T12:27:50","slug":"find-the-missing-endpoint-if-s-is-the-midpoint-of-rt-r-94-and-s2-1-find-t","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/06\/find-the-missing-endpoint-if-s-is-the-midpoint-of-rt-r-94-and-s2-1-find-t\/","title":{"rendered":"find the missing endpoint if s is the midpoint of rt r(-9,4) and s(2,-1) ; find T"},"content":{"rendered":"\n<p>find the missing endpoint if s is the midpoint of rt r(-9,4) and s(2,-1) ; find T<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find the missing endpoint T(x,y)T(x, y)T(x,y) given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>One endpoint R(\u22129,4)R(-9, 4)R(\u22129,4)<\/li>\n\n\n\n<li>Midpoint S(2,\u22121)S(2, -1)S(2,\u22121)<\/li>\n<\/ul>\n\n\n\n<p>We use the <strong>midpoint formula<\/strong>:S=(x1+x22,y1+y22)S = \\left( \\frac{x_1 + x_2}{2}, \\frac{y_1 + y_2}{2} \\right)S=(2&#215;1\u200b+x2\u200b\u200b,2y1\u200b+y2\u200b\u200b)<\/p>\n\n\n\n<p>Let R=(x1,y1)=(\u22129,4)R = (x_1, y_1) = (-9, 4)R=(x1\u200b,y1\u200b)=(\u22129,4), and let T=(x2,y2)T = (x_2, y_2)T=(x2\u200b,y2\u200b). We&#8217;re told the midpoint S=(2,\u22121)S = (2, -1)S=(2,\u22121). Plug the known values into the formula:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Solve for x2x_2x2\u200b<\/h3>\n\n\n\n<p>\u22129+x22=2\\frac{-9 + x_2}{2} = 22\u22129+x2\u200b\u200b=2<\/p>\n\n\n\n<p>Multiply both sides by 2:\u22129+x2=4-9 + x_2 = 4\u22129+x2\u200b=4<\/p>\n\n\n\n<p>Add 9 to both sides:x2=13x_2 = 13&#215;2\u200b=13<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Solve for y2y_2y2\u200b<\/h3>\n\n\n\n<p>4+y22=\u22121\\frac{4 + y_2}{2} = -124+y2\u200b\u200b=\u22121<\/p>\n\n\n\n<p>Multiply both sides by 2:4+y2=\u221224 + y_2 = -24+y2\u200b=\u22122<\/p>\n\n\n\n<p>Subtract 4 from both sides:y2=\u22126y_2 = -6y2\u200b=\u22126<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>T=(13,\u22126)T = (13, -6)T=(13,\u22126)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"> Explanation:<\/h3>\n\n\n\n<p>This formula essentially means the midpoint lies exactly halfway between the two endpoints. If one endpoint and the midpoint are known, we can treat this formula like a system of equations to solve for the missing endpoint.<\/p>\n\n\n\n<p>To find a missing endpoint of a line segment when the midpoint and one endpoint are given, we use the <strong>midpoint formula<\/strong>, which finds the average of the x-coordinates and y-coordinates of two endpoints:Midpoint=(x1+x22,y1+y22)\\text{Midpoint} = \\left( \\frac{x_1 + x_2}{2}, \\frac{y_1 + y_2}{2} \\right)Midpoint=(2&#215;1\u200b+x2\u200b\u200b,2y1\u200b+y2\u200b\u200b)<\/p>\n\n\n\n<p>In this problem, we are given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>One endpoint R(\u22129,4)R(-9, 4)R(\u22129,4)<\/li>\n\n\n\n<li>The midpoint S(2,\u22121)S(2, -1)S(2,\u22121)<\/li>\n<\/ul>\n\n\n\n<p>Let T(x,y)T(x, y)T(x,y) be the missing endpoint.<\/p>\n\n\n\n<p>We apply the midpoint formula:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For the x-coordinates: \u22129+x2=2\\frac{-9 + x}{2} = 22\u22129+x\u200b=2. Solving gives x=13x = 13x=13.<\/li>\n\n\n\n<li>For the y-coordinates: 4+y2=\u22121\\frac{4 + y}{2} = -124+y\u200b=\u22121. Solving gives y=\u22126y = -6y=\u22126.<\/li>\n<\/ul>\n\n\n\n<p>So, the coordinates of the missing endpoint TTT are (13,\u22126)(13, -6)(13,\u22126).<\/p>\n\n\n\n<p>This process is reliable and works for any situation involving midpoints and endpoints on the coordinate plane. It helps in geometry problems, computer graphics, engineering, and real-world spatial reasoning tasks.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner9-133.jpeg\" alt=\"\" class=\"wp-image-227745\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>find the missing endpoint if s is the midpoint of rt r(-9,4) and s(2,-1) ; find T The Correct Answer and Explanation is: To find the missing endpoint T(x,y)T(x, y)T(x,y) given: We use the midpoint formula:S=(x1+x22,y1+y22)S = \\left( \\frac{x_1 + x_2}{2}, \\frac{y_1 + y_2}{2} \\right)S=(2&#215;1\u200b+x2\u200b\u200b,2y1\u200b+y2\u200b\u200b) Let R=(x1,y1)=(\u22129,4)R = (x_1, y_1) = (-9, 4)R=(x1\u200b,y1\u200b)=(\u22129,4), and let [&hellip;]<\/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-227744","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227744","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=227744"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227744\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=227744"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=227744"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=227744"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}