{"id":266153,"date":"2025-07-22T16:29:38","date_gmt":"2025-07-22T16:29:38","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=266153"},"modified":"2025-07-22T16:29:42","modified_gmt":"2025-07-22T16:29:42","slug":"find-the-midpoint-of-the-segment-with-the-following-endpoints-1-10-and-8-4","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/22\/find-the-midpoint-of-the-segment-with-the-following-endpoints-1-10-and-8-4\/","title":{"rendered":"&#8216;Find the midpoint of the segment with the following endpoints (1,-10) and (8,-4)&#8217;"},"content":{"rendered":"\n<p>&#8216;Find the midpoint of the segment with the following endpoints (1,-10) and (8,-4)&#8217;<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find the midpoint of a line segment, you can use the midpoint formula, which is: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>Where (x1,y1)(x_1, y_1)(x1\u200b,y1\u200b) and (x2,y2)(x_2, y_2)(x2\u200b,y2\u200b) are the coordinates of the two endpoints.<\/p>\n\n\n\n<p>Given endpoints:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(x1,y1)=(1,\u221210)(x_1, y_1) = (1, -10)(x1\u200b,y1\u200b)=(1,\u221210)<\/li>\n\n\n\n<li>(x2,y2)=(8,\u22124)(x_2, y_2) = (8, -4)(x2\u200b,y2\u200b)=(8,\u22124)<\/li>\n<\/ul>\n\n\n\n<p>Now, applying the midpoint formula:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>For the x-coordinate of the midpoint:<\/li>\n<\/ol>\n\n\n\n<p>x1+x22=1+82=92=4.5\\frac{x_1 + x_2}{2} = \\frac{1 + 8}{2} = \\frac{9}{2} = 4.52&#215;1\u200b+x2\u200b\u200b=21+8\u200b=29\u200b=4.5<\/p>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li>For the y-coordinate of the midpoint:<\/li>\n<\/ol>\n\n\n\n<p>y1+y22=\u221210+(\u22124)2=\u2212142=\u22127\\frac{y_1 + y_2}{2} = \\frac{-10 + (-4)}{2} = \\frac{-14}{2} = -72y1\u200b+y2\u200b\u200b=2\u221210+(\u22124)\u200b=2\u221214\u200b=\u22127<\/p>\n\n\n\n<p>Therefore, the midpoint of the segment is:(4.5,\u22127)\\boxed{(4.5, -7)}(4.5,\u22127)\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>The midpoint of a segment is essentially the &#8220;average&#8221; of the x-coordinates and y-coordinates of the two endpoints. By finding the mean of the x-values and the mean of the y-values, you get the exact point that divides the segment into two equal lengths. This point is equidistant from both endpoints.<\/p>\n\n\n\n<p>This method works for any two points in a two-dimensional coordinate system. It is often useful in geometry and can help you find the center of a shape or the balance point of a line.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1547.jpeg\" alt=\"\" class=\"wp-image-266154\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>&#8216;Find the midpoint of the segment with the following endpoints (1,-10) and (8,-4)&#8217; The Correct Answer and Explanation is: To find the midpoint of a line segment, you can use the midpoint formula, which is: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) Where (x1,y1)(x_1, y_1)(x1\u200b,y1\u200b) and (x2,y2)(x_2, y_2)(x2\u200b,y2\u200b) are the coordinates of the [&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-266153","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/266153","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=266153"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/266153\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=266153"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=266153"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=266153"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}