{"id":196413,"date":"2025-03-05T03:57:47","date_gmt":"2025-03-05T03:57:47","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=196413"},"modified":"2025-03-05T03:57:50","modified_gmt":"2025-03-05T03:57:50","slug":"what-is-the-most-precise-name-for-quadrilateral-abcd-with-vertices-a-2-4-b3-4-c6-0-and-d1-0","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/05\/what-is-the-most-precise-name-for-quadrilateral-abcd-with-vertices-a-2-4-b3-4-c6-0-and-d1-0\/","title":{"rendered":"What is the most precise name for quadrilateral ABCD with vertices A(-2, 4), B(3, 4), C(6, 0), and D(1, 0)"},"content":{"rendered":"\n<p>What is the most precise name for quadrilateral ABCD with vertices A(-2, 4), B(3, 4), C(6, 0), and D(1, 0)?<br>A. rhombus<br>B. square<br>C. parallelogram<br>D. rectangle<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>\ue200i\ue202turn0image1\ue201Quadrilateral ABCD, with vertices A(-2, 4), B(3, 4), C(6, 0), and D(1, 0), is best classified as a <strong>rectangle<\/strong>. Here&#8217;s a detailed explanation:\ue206<\/p>\n\n\n\n<p><strong>Step 1: Plotting the Vertices<\/strong><\/p>\n\n\n\n<p>First, plot the given vertices on the Cartesian plane:\ue206<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A(-2, 4)\ue206<\/li>\n\n\n\n<li>B(3, 4)\ue206<\/li>\n\n\n\n<li>C(6, 0)\ue206<\/li>\n\n\n\n<li>D(1, 0)\ue206<\/li>\n<\/ul>\n\n\n\n<p>Connecting these points in order forms quadrilateral ABCD.\ue206<\/p>\n\n\n\n<p><strong>Step 2: Calculating the Slopes of the Sides<\/strong><\/p>\n\n\n\n<p>To determine the nature of the quadrilateral, calculate the slopes of its sides:\ue206<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Slope of AB<\/strong>:<br>[ \\text{Slope of AB} = \\frac{4 &#8211; 4}{3 &#8211; (-2)} = \\frac{0}{5} = 0 ]\ue206<br>This indicates that line AB is horizontal.\ue206<\/li>\n\n\n\n<li><strong>Slope of BC<\/strong>:<br>[ \\text{Slope of BC} = \\frac{0 &#8211; 4}{6 &#8211; 3} = \\frac{-4}{3} ]\ue206<br>This line has a negative slope, indicating it&#8217;s neither horizontal nor vertical.\ue206<\/li>\n\n\n\n<li><strong>Slope of CD<\/strong>:<br>[ \\text{Slope of CD} = \\frac{0 &#8211; 0}{1 &#8211; 6} = \\frac{0}{-5} = 0 ]\ue206<br>This indicates that line CD is horizontal.\ue206<\/li>\n\n\n\n<li><strong>Slope of DA<\/strong>:<br>[ \\text{Slope of DA} = \\frac{4 &#8211; 0}{-2 &#8211; 1} = \\frac{4}{-3} ]\ue206<br>This line has a negative slope, similar to BC.\ue206<\/li>\n<\/ul>\n\n\n\n<p><strong>Step 3: Analyzing the Slopes<\/strong><\/p>\n\n\n\n<p>The slopes of opposite sides are equal:\ue206<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Slope of AB = Slope of CD = 0 (both horizontal)\ue206<\/li>\n\n\n\n<li>Slope of BC = Slope of DA = -4\/3\ue206<\/li>\n<\/ul>\n\n\n\n<p>This confirms that opposite sides are parallel, a defining property of parallelograms.\ue206<\/p>\n\n\n\n<p><strong>Step 4: Checking for Right Angles<\/strong><\/p>\n\n\n\n<p>To verify if the quadrilateral is a rectangle, check for perpendicular adjacent sides by calculating the product of their slopes:\ue206<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Product of slopes of AB and BC:\ue206<br>[ 0 \\times \\left(-\\frac{4}{3}\\right) = 0 ]\ue206<br>Since the product is zero, lines AB and BC are perpendicular, confirming a right angle at vertex B.\ue206<\/li>\n\n\n\n<li>Product of slopes of BC and CD:\ue206<br>[ \\left(-\\frac{4}{3}\\right) \\times 0 = 0 ]\ue206<br>This indicates a right angle at vertex C.\ue206<\/li>\n\n\n\n<li>Product of slopes of CD and DA:\ue206<br>[ 0 \\times \\left(-\\frac{4}{3}\\right) = 0 ]\ue206<br>This indicates a right angle at vertex D.\ue206<\/li>\n\n\n\n<li>Product of slopes of DA and AB:\ue206<br>[ \\left(-\\frac{4}{3}\\right) \\times 0 = 0 ]\ue206<br>This indicates a right angle at vertex A.\ue206<\/li>\n<\/ul>\n\n\n\n<p>Since all adjacent sides are perpendicular, quadrilateral ABCD has four right angles, confirming it is a rectangle.\ue206<\/p>\n\n\n\n<p><strong>Conclusion<\/strong><\/p>\n\n\n\n<p>Based on the calculations and analyses, quadrilateral ABCD is a rectangle. Therefore, the correct answer is D.\ue206<\/p>\n\n\n\n<p><strong>Visual Representation<\/strong><\/p>\n\n\n\n<p>Below is a graphical representation of quadrilateral ABCD on the Cartesian plane:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/03\/image-184.png\" alt=\"\" class=\"wp-image-196414\"\/><\/figure>\n\n\n\n<p><em>Note: The image above is sourced from a related problem with similar vertex coordinates.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is the most precise name for quadrilateral ABCD with vertices A(-2, 4), B(3, 4), C(6, 0), and D(1, 0)?A. rhombusB. squareC. parallelogramD. rectangle The Correct Answer and Explanation is : \ue200i\ue202turn0image1\ue201Quadrilateral ABCD, with vertices A(-2, 4), B(3, 4), C(6, 0), and D(1, 0), is best classified as a rectangle. Here&#8217;s a detailed explanation:\ue206 Step [&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-196413","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196413","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=196413"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196413\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=196413"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=196413"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=196413"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}