{"id":248360,"date":"2025-07-08T10:29:32","date_gmt":"2025-07-08T10:29:32","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=248360"},"modified":"2025-07-08T10:29:34","modified_gmt":"2025-07-08T10:29:34","slug":"reflection-across-x-3-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/08\/reflection-across-x-3-2\/","title":{"rendered":"Reflection across x = -3"},"content":{"rendered":"\n

reflection across x = -3 A graph is shown with multiple geometric points forming a shape. The points are labeled I, W, S, and P on a Cartesian plane.<\/p>\n\n\n\n

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

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

Here are the coordinates of the reflected quadrilateral:
I'(-1, -1)<\/strong>
P'(-2, -2)<\/strong>
S'(-4, 1)<\/strong>
W'(-4, 3)<\/strong><\/p>\n\n\n\n

Explanation<\/h3>\n\n\n\n

To find the reflection of the quadrilateral IWSP across the vertical line x = -3, we need to determine the new coordinates for each of its vertices. A reflection is a type of geometric transformation that flips a figure over a line, known as the line of reflection, to create a mirror image. This process is a rigid transformation, which means the resulting figure, I’W’S’P’, will have the same size and shape as the original.<\/p>\n\n\n\n

First, we must identify the coordinates of the original vertices by reading the graph:<\/p>\n\n\n\n

    \n
  • I<\/strong>\u00a0is located at (-5, -1).<\/li>\n\n\n\n
  • P<\/strong>\u00a0is located at (-4, -2).<\/li>\n\n\n\n
  • S<\/strong>\u00a0is located at (-2, 1).<\/li>\n\n\n\n
  • W<\/strong>\u00a0is located at (-2, 3).<\/li>\n<\/ul>\n\n\n\n

    The line of reflection is the vertical line x = -3. For any reflection across a vertical line, the y-coordinate of each point remains unchanged. The new x-coordinate is found by measuring the horizontal distance from the original point to the line of reflection and then moving that same distance to the opposite side of the line.<\/p>\n\n\n\n

    Let’s apply this process to each vertex:<\/p>\n\n\n\n

      \n
    • Point I(-5, -1):<\/strong>\u00a0The x-coordinate is -5. The horizontal distance from x = -5 to the line x = -3 is 2 units to the left. To reflect this point, we move 2 units to the right of the line x = -3. The new x-coordinate is -3 + 2 = -1. The y-coordinate stays the same. Therefore, the reflected point\u00a0I’ is (-1, -1)<\/strong>.<\/li>\n\n\n\n
    • Point P(-4, -2):<\/strong>\u00a0The x-coordinate is -4, which is 1 unit to the left of the line x = -3. The reflection will be 1 unit to the right of the line. The new x-coordinate is -3 + 1 = -2. The y-coordinate remains -2. Thus, the reflected point\u00a0P’ is (-2, -2)<\/strong>.<\/li>\n\n\n\n
    • Point S(-2, 1):<\/strong>\u00a0The x-coordinate is -2, which is 1 unit to the right of the line x = -3. The reflection will be 1 unit to the left of the line. The new x-coordinate is -3 – 1 = -4. The y-coordinate remains 1. So, the reflected point\u00a0S’ is (-4, 1)<\/strong>.<\/li>\n\n\n\n
    • Point W(-2, 3):<\/strong>\u00a0The x-coordinate is -2, which is 1 unit to the right of the line x = -3. The reflection will be 1 unit to the left of the line. The new x-coordinate is -3 – 1 = -4. The y-coordinate remains 3. Consequently, the reflected point\u00a0W’ is (-4, 3)<\/strong>.<\/li>\n<\/ul>\n\n\n\n

      By connecting these new points, we form the reflected quadrilateral I’W’S’P’.<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      reflection across x = -3 A graph is shown with multiple geometric points forming a shape. The points are labeled I, W, S, and P on a Cartesian plane. The Correct Answer and Explanation is: Here are the coordinates of the reflected quadrilateral:I'(-1, -1)P'(-2, -2)S'(-4, 1)W'(-4, 3) Explanation To find the reflection of the quadrilateral […]<\/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-248360","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248360","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=248360"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248360\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=248360"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=248360"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=248360"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}