{"id":225666,"date":"2025-06-04T11:24:19","date_gmt":"2025-06-04T11:24:19","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=225666"},"modified":"2025-06-04T11:24:21","modified_gmt":"2025-06-04T11:24:21","slug":"this-graph-has-rotational-symmetry-about-the-point","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/04\/this-graph-has-rotational-symmetry-about-the-point\/","title":{"rendered":"This graph has rotational symmetry about the point"},"content":{"rendered":"\n<p>This graph has rotational symmetry about the point<\/p>\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<h3 class=\"wp-block-heading\">\u2705 <strong>Correct Answer: (0, 0)<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udcd8 <strong>Explanation <\/strong><\/h3>\n\n\n\n<p>The graph in the image shows a smooth S-shaped curve passing through the origin (0,0)(0, 0), increasing from the bottom left to the top right. This is the characteristic shape of <strong>odd functions<\/strong> such as y=x3y = x^3 or similar cubic functions.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udd04 <strong>What Is Rotational Symmetry?<\/strong><\/h3>\n\n\n\n<p>A graph has <strong>rotational symmetry<\/strong> about a point if rotating the graph <strong>180 degrees<\/strong> around that point results in the same graph. In simpler terms, the graph looks identical upside down if you spin it halfway around that central point.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udccc <strong>Identifying the Center of Rotation<\/strong><\/h3>\n\n\n\n<p>To find the center of rotational symmetry:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Look for a point where the graph is \u201cbalanced.\u201d<\/li>\n\n\n\n<li>In this case, the curve passes through the origin and mirrors itself diagonally.<\/li>\n\n\n\n<li>If you rotate the graph 180\u00b0 about the <strong>origin (0, 0)<\/strong>, the top right part maps onto the bottom left, and vice versa.<\/li>\n<\/ol>\n\n\n\n<p>This shows the graph is symmetric around the origin.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83e\udde0 <strong>Mathematical Reasoning<\/strong><\/h3>\n\n\n\n<p>The graph represents an <strong>odd function<\/strong>. A function is odd if: f(\u2212x)=\u2212f(x)f(-x) = -f(x)<\/p>\n\n\n\n<p>This property means that if you take a point (x,y)(x, y) on the graph, the point (\u2212x,\u2212y)(-x, -y) is also on the graph \u2014 which is exactly what happens with 180\u00b0 rotational symmetry about the origin.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udd0d <strong>Conclusion<\/strong><\/h3>\n\n\n\n<p>The correct point of rotational symmetry is:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>(0,0)\\boxed{(0, 0)}<\/p>\n<\/blockquote>\n\n\n\n<p>This symmetry is a defining feature of many cubic and other odd-degree functions, and recognizing it helps understand their graphical behavior.<\/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-banner4-342.jpeg\" alt=\"\" class=\"wp-image-225667\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>This graph has rotational symmetry about the point The Correct Answer and Explanation is: \u2705 Correct Answer: (0, 0) \ud83d\udcd8 Explanation The graph in the image shows a smooth S-shaped curve passing through the origin (0,0)(0, 0), increasing from the bottom left to the top right. This is the characteristic shape of odd functions such [&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-225666","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225666","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=225666"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225666\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=225666"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=225666"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=225666"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}