{"id":231397,"date":"2025-06-11T04:20:06","date_gmt":"2025-06-11T04:20:06","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=231397"},"modified":"2025-06-11T04:20:10","modified_gmt":"2025-06-11T04:20:10","slug":"rotate-pqr-270counterclockwise-around-the-origin","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/11\/rotate-pqr-270counterclockwise-around-the-origin\/","title":{"rendered":"Rotate PQR 270counterclockwise around the origin."},"content":{"rendered":"\n<p>Rotate PQR 270<br>counterclockwise around the origin.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/image-352-1024x417.png\" alt=\"\" class=\"wp-image-231398\"\/><\/figure>\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><strong>The vertices of the rotated triangle, \u0394P&#8217;Q&#8217;R&#8217;, are:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>P&#8217; (20, 10)<\/strong><\/li>\n\n\n\n<li><strong>Q&#8217; (10, 20)<\/strong><\/li>\n\n\n\n<li><strong>R&#8217; (10, 10)<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation<\/strong><\/h3>\n\n\n\n<p>The objective is to rotate triangle PQR by 270 degrees counterclockwise around the origin (0, 0). A rotation is a rigid transformation, which means the size and shape of the triangle will be preserved; only its orientation and position will change. The process involves three main steps: identifying the original coordinates, applying the rotation rule, and determining the new coordinates.<\/p>\n\n\n\n<p><strong>Step 1: Determine the coordinates of the original vertices.<\/strong><br>First, we must identify the coordinates of the vertices P, Q, and R from the graph. By observing the axes, we can see that each grid line represents 5 units.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Vertex P<\/strong>\u00a0is located 2 grid lines to the left of the y-axis and 4 grid lines above the x-axis. Therefore, its coordinates are P = (-10, 20).<\/li>\n\n\n\n<li><strong>Vertex Q<\/strong>\u00a0is located 4 grid lines to the left of the y-axis and 2 grid lines above the x-axis. Its coordinates are Q = (-20, 10).<\/li>\n\n\n\n<li><strong>Vertex R<\/strong>\u00a0is located 2 grid lines to the left of the y-axis and 2 grid lines above the x-axis. Its coordinates are R = (-10, 10).<\/li>\n<\/ul>\n\n\n\n<p><strong>Step 2: Understand the rule for a 270\u00b0 counterclockwise rotation.<\/strong><br>A 270\u00b0 counterclockwise rotation around the origin follows a specific algebraic rule. For any point with coordinates (x, y), a 270\u00b0 counterclockwise rotation transforms it to a new point with coordinates (y, -x). This means the original x and y values swap positions, and the new y-coordinate becomes the opposite of the original x-coordinate. This transformation is also equivalent to a 90\u00b0 clockwise rotation.<\/p>\n\n\n\n<p><strong>Step 3: Apply the rotation rule to each vertex.<\/strong><br>We now apply the rule (x, y) \u2192 (y, -x) to each vertex of \u0394PQR to find the coordinates of the rotated triangle, \u0394P&#8217;Q&#8217;R&#8217;.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>For P(-10, 20):<\/strong><br>The new coordinates P&#8217; will be (20, -(-10)), which simplifies to\u00a0<strong>P'(20, 10)<\/strong>.<\/li>\n\n\n\n<li><strong>For Q(-20, 10):<\/strong><br>The new coordinates Q&#8217; will be (10, -(-20)), which simplifies to\u00a0<strong>Q'(10, 20)<\/strong>.<\/li>\n\n\n\n<li><strong>For R(-10, 10):<\/strong><br>The new coordinates R&#8217; will be (10, -(-10)), which simplifies to\u00a0<strong>R'(10, 10)<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>By completing these steps, we have successfully rotated \u0394PQR 270\u00b0 counterclockwise around the origin to its new position, \u0394P&#8217;Q&#8217;R&#8217;, with vertices at P'(20, 10), Q'(10, 20), and R'(10, 10).<\/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-banner4-892.jpeg\" alt=\"\" class=\"wp-image-231399\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Rotate PQR 270counterclockwise around the origin. The Correct Answer and Explanation is: The vertices of the rotated triangle, \u0394P&#8217;Q&#8217;R&#8217;, are: Explanation The objective is to rotate triangle PQR by 270 degrees counterclockwise around the origin (0, 0). A rotation is a rigid transformation, which means the size and shape of the triangle will be preserved; [&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-231397","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/231397","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=231397"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/231397\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=231397"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=231397"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=231397"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}