{"id":157122,"date":"2024-10-18T19:32:06","date_gmt":"2024-10-18T19:32:06","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=157122"},"modified":"2024-10-18T19:32:09","modified_gmt":"2024-10-18T19:32:09","slug":"to-reflect-a-point-across-the-line-y-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/18\/to-reflect-a-point-across-the-line-y-2\/","title":{"rendered":"To reflect a point across the line y = 2"},"content":{"rendered":"\n

To reflect a point across the line y = 2, we simply take the y-coordinate of the point and subtract it from 2?<\/p>\n\n\n\n

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

To reflect a point across the line ( y = 2 ), you indeed need to consider the y-coordinate of the point, but the process involves more than just subtracting it from 2. Here\u2019s the correct approach:<\/p>\n\n\n\n

    \n
  1. Identify the Point:<\/strong> Let\u2019s say you have a point ( P(x, y) ) that you want to reflect across the line ( y = 2 ).<\/li>\n\n\n\n
  2. Find the Distance to the Line:<\/strong> The line ( y = 2 ) is horizontal, so the distance from the point ( P ) to the line is given by ( d = y – 2 ) (if ( y ) is above the line) or ( d = 2 – y ) (if ( y ) is below the line).<\/li>\n\n\n\n
  3. Calculate the Reflected Point:<\/strong> The reflected point ( P’ ) will be located the same distance from the line ( y = 2 ) but on the opposite side. Thus, the y-coordinate of the reflected point ( P’ ) can be calculated as follows:<\/li>\n<\/ol>\n\n\n\n
      \n
    • If ( y ) is greater than 2 (above the line):
      [ P'(x, y’) = \\left(x, 2 – (y – 2)\\right) = \\left(x, 4 – y\\right) ]<\/li>\n\n\n\n
    • If ( y ) is less than 2 (below the line):
      [ P'(x, y’) = \\left(x, 2 + (2 – y)\\right) = \\left(x, 4 – y\\right) ]<\/li>\n<\/ul>\n\n\n\n

      In both cases, the formula simplifies to the same result for the reflected point:
      [ P'(x, y’) = (x, 4 – y) ]<\/p>\n\n\n\n

      Example:<\/strong> If the point is ( P(3, 5) ):<\/p>\n\n\n\n

        \n
      • The distance from ( P ) to the line ( y = 2 ) is ( 5 – 2 = 3 ).<\/li>\n\n\n\n
      • To reflect it, calculate the new y-coordinate:
        [ P'(3, y’) = (3, 4 – 5) = (3, -1) ]
        So the reflected point across the line ( y = 2 ) is ( P'(3, -1) ).<\/li>\n<\/ul>\n\n\n\n

        This process can be visualized geometrically: the original point and its reflection are equidistant from the line ( y = 2 ), ensuring a symmetric relationship with respect to the line of reflection.<\/p>\n","protected":false},"excerpt":{"rendered":"

        To reflect a point across the line y = 2, we simply take the y-coordinate of the point and subtract it from 2? The Correct Answer and Explanation is : To reflect a point across the line ( y = 2 ), you indeed need to consider the y-coordinate of the point, but the process […]<\/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-157122","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/157122","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=157122"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/157122\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=157122"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=157122"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=157122"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}