{"id":188961,"date":"2025-02-08T09:23:55","date_gmt":"2025-02-08T09:23:55","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=188961"},"modified":"2025-02-08T09:23:57","modified_gmt":"2025-02-08T09:23:57","slug":"find-the-midpoint-of-the-line-segment-shown-below","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/08\/find-the-midpoint-of-the-line-segment-shown-below\/","title":{"rendered":"Find The Midpoint Of The Line Segment Shown Below"},"content":{"rendered":"\n

Find The Midpoint Of The Line Segment Shown Below<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Midpoint =<\/p>\n\n\n\n

The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

To find the midpoint of a line segment, we use the midpoint formula, which calculates the point exactly halfway between two given points. This point is equidistant from both endpoints and bisects the segment.<\/p>\n\n\n\n

Midpoint Formula:<\/strong><\/p>\n\n\n\n

If the endpoints of the line segment are ( A(x_1, y_1) ) and ( B(x_2, y_2) ), the midpoint ( M ) is given by:<\/p>\n\n\n\n

[ M = \\left( \\frac{x_1 + x_2}{2}, \\frac{y_1 + y_2}{2} \\right) ]<\/p>\n\n\n\n

Steps to Calculate the Midpoint:<\/strong><\/p>\n\n\n\n

    \n
  1. Identify the Coordinates:<\/strong> Determine the coordinates of the two endpoints.<\/li>\n\n\n\n
  2. Add the x-Coordinates:<\/strong> Sum the x-coordinates of the two points.<\/li>\n\n\n\n
  3. Divide by 2:<\/strong> Divide the sum of the x-coordinates by 2 to find the x-coordinate of the midpoint.<\/li>\n\n\n\n
  4. Add the y-Coordinates:<\/strong> Sum the y-coordinates of the two points.<\/li>\n\n\n\n
  5. Divide by 2:<\/strong> Divide the sum of the y-coordinates by 2 to find the y-coordinate of the midpoint.<\/li>\n\n\n\n
  6. Combine the Results:<\/strong> The midpoint is the point with the x and y coordinates obtained in steps 3 and 5.<\/li>\n<\/ol>\n\n\n\n

    Example:<\/strong><\/p>\n\n\n\n

    Consider two points ( A(2, 3) ) and ( B(4, 7) ).<\/p>\n\n\n\n

      \n
    1. Add the x-Coordinates:<\/strong> ( 2 + 4 = 6 )<\/li>\n\n\n\n
    2. Divide by 2:<\/strong> ( \\frac{6}{2} = 3 )<\/li>\n\n\n\n
    3. Add the y-Coordinates:<\/strong> ( 3 + 7 = 10 )<\/li>\n\n\n\n
    4. Divide by 2:<\/strong> ( \\frac{10}{2} = 5 )<\/li>\n<\/ol>\n\n\n\n

      Therefore, the midpoint ( M ) is ( (3, 5) ).<\/p>\n\n\n\n

      Applications of the Midpoint Formula:<\/strong><\/p>\n\n\n\n

        \n
      • Geometry:<\/strong> Determining the center of a line segment, which is essential in constructions and proofs.<\/li>\n\n\n\n
      • Physics:<\/strong> Calculating the center of mass for two-point masses.<\/li>\n\n\n\n
      • Computer Graphics:<\/strong> Finding the center point between two pixels or objects.<\/li>\n\n\n\n
      • Navigation:<\/strong> Identifying the central point between two locations.<\/li>\n<\/ul>\n\n\n\n

        Understanding the midpoint formula is fundamental in various fields, as it provides a straightforward method to find the central point between two locations, aiding in analysis and design.<\/p>\n\n\n\n

        For a visual explanation, you might find this video helpful:<\/p>\n\n\n\n

        \ue200video\ue202Finding the midpoint of a line segment\ue202turn0search5\ue201<\/p>\n","protected":false},"excerpt":{"rendered":"

        Find The Midpoint Of The Line Segment Shown Below Midpoint = The Correct Answer and Explanation is : To find the midpoint of a line segment, we use the midpoint formula, which calculates the point exactly halfway between two given points. This point is equidistant from both endpoints and bisects the segment. Midpoint Formula: If […]<\/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-188961","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188961","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=188961"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188961\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=188961"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=188961"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=188961"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}