{"id":226501,"date":"2025-06-05T10:20:14","date_gmt":"2025-06-05T10:20:14","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=226501"},"modified":"2025-06-05T10:20:16","modified_gmt":"2025-06-05T10:20:16","slug":"figures-in-the-coordinate-plane-lmnp-is-a-parallelogram","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/05\/figures-in-the-coordinate-plane-lmnp-is-a-parallelogram\/","title":{"rendered":"Figures in the Coordinate Plane LMNP is a parallelogram."},"content":{"rendered":"\n

Figures in the Coordinate Plane LMNP is a parallelogram. What additional information would prove that LMNP is a rectangle? The length of LM is
and the length of MN is
. The slope of LP and MN is -2. LM \\parallel PN LP \\perp P<\/p>\n\n\n\n

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

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

To determine which additional information would prove that LMNP is a rectangle<\/strong>, let\u2019s first review what makes a parallelogram<\/strong> a rectangle<\/strong>:<\/p>\n\n\n\n

A parallelogram<\/strong> becomes a rectangle<\/strong> when:<\/p>\n\n\n\n

    \n
  1. All angles are right angles<\/strong>, or<\/li>\n\n\n\n
  2. Adjacent sides are perpendicular<\/strong>, or<\/li>\n\n\n\n
  3. Diagonals are equal and bisect each other at right angles<\/strong>, or<\/li>\n\n\n\n
  4. One angle is a right angle<\/strong> (which implies all others are right angles due to parallel opposite sides).<\/li>\n<\/ol>\n\n\n\n

    Now, in the given image, LMNP<\/strong> is already a parallelogram<\/strong>, so:<\/p>\n\n\n\n

      \n
    • Opposite sides are parallel.<\/li>\n\n\n\n
    • Opposite sides are equal in length.<\/li>\n<\/ul>\n\n\n\n

      To prove that this parallelogram is a rectangle<\/strong>, we need evidence of right angles<\/strong>.<\/p>\n\n\n\n

      The correct answer:<\/h3>\n\n\n\n

      “LP \u22a5 PN”<\/strong> (LP is perpendicular to PN)<\/p>\n\n\n\n

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

      In coordinate geometry, a rectangle is a special type of parallelogram where adjacent sides meet at right angles (90\u00b0). The given figure, LMNP, is a parallelogram, which means opposite sides are parallel and equal in length, but this alone does not confirm the shape is a rectangle.<\/p>\n\n\n\n

      To confirm LMNP is a rectangle, we need to prove that at least one angle is a right angle. In coordinate geometry, this can be done by verifying the perpendicularity<\/strong> of adjacent sides using slopes. If the product of the slopes of two adjacent sides is -1<\/strong>, they are perpendicular.<\/p>\n\n\n\n

      Among the answer choices:<\/p>\n\n\n\n

        \n
      • Length of sides<\/strong> only tells us about the size, not the shape.<\/li>\n\n\n\n
      • Same slope for LP and MN<\/strong> only shows they are parallel, not perpendicular.<\/li>\n\n\n\n
      • LM \u2225 PN<\/strong> again confirms parallelism, not perpendicularity.<\/li>\n<\/ul>\n\n\n\n

        However, “LP \u22a5 PN”<\/strong> (LP is perpendicular to PN) tells us that two adjacent sides form a right angle<\/strong>, which is exactly what\u2019s needed to show that the parallelogram is a rectangle<\/strong>. If one interior angle is a right angle in a parallelogram, then all interior angles must be right angles, confirming the shape is a rectangle.<\/p>\n\n\n\n

        Therefore, the additional information that would prove LMNP is a rectangle is:<\/p>\n\n\n\n

        \u2705 LP \u22a5 PN<\/strong> (correct answer)<\/p>\n\n\n\n

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

        Figures in the Coordinate Plane LMNP is a parallelogram. What additional information would prove that LMNP is a rectangle? The length of LM isand the length of MN is. The slope of LP and MN is -2. LM \\parallel PN LP \\perp P The Correct Answer and Explanation is: To determine which additional information would […]<\/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-226501","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/226501","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=226501"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/226501\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=226501"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=226501"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=226501"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}