{"id":280908,"date":"2025-08-05T08:14:49","date_gmt":"2025-08-05T08:14:49","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=280908"},"modified":"2025-08-05T08:14:51","modified_gmt":"2025-08-05T08:14:51","slug":"using-midpoint-and-distance-formulas-section-exercises-1-3-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/08\/05\/using-midpoint-and-distance-formulas-section-exercises-1-3-2\/","title":{"rendered":"\u00a0Using Midpoint and Distance Formulas > Section Exercises 1.3 2"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/08\/image-501.png\" alt=\"\" class=\"wp-image-280909\"\/><\/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>The correct answer is&nbsp;<strong>10<\/strong>.<\/p>\n\n\n\n<p>To find the distance between two points, A(13, 2) and B(7, 10), in a two-dimensional plane, we use the distance formula. This formula is derived from the Pythagorean theorem and is expressed as:<\/p>\n\n\n\n<p>d = \u221a[(x\u2082 &#8211; x\u2081)\u00b2 + (y\u2082 &#8211; y\u2081)\u00b2]<\/p>\n\n\n\n<p>Here, (x\u2081, y\u2081) represents the coordinates of the first point, A, and (x\u2082, y\u2082) represents the coordinates of the second point, B. The &#8216;d&#8217; stands for the distance between them.<\/p>\n\n\n\n<p>First, we identify the coordinates from the given points:<br>For point A(13, 2): x\u2081 = 13 and y\u2081 = 2.<br>For point B(7, 10): x\u2082 = 7 and y\u2082 = 10.<\/p>\n\n\n\n<p>Next, we substitute these values into the distance formula:<br>d = \u221a[(7 &#8211; 13)\u00b2 + (10 &#8211; 2)\u00b2]<\/p>\n\n\n\n<p>Now, we perform the calculations inside the parentheses:<br>The difference in the x-coordinates is 7 &#8211; 13 = -6.<br>The difference in the y-coordinates is 10 &#8211; 2 = 8.<\/p>\n\n\n\n<p>Substituting these results back into the formula gives us:<br>d = \u221a[(-6)\u00b2 + (8)\u00b2]<\/p>\n\n\n\n<p>Next, we square each of these values. Remember that squaring a negative number results in a positive number:<br>(-6)\u00b2 = 36<br>(8)\u00b2 = 64<\/p>\n\n\n\n<p>Now the equation looks like this:<br>d = \u221a[36 + 64]<\/p>\n\n\n\n<p>We then add the two numbers inside the square root symbol:<br>36 + 64 = 100<\/p>\n\n\n\n<p>Finally, we find the square root of the sum:<br>d = \u221a100<br>d = 10<\/p>\n\n\n\n<p>Therefore, the distance between point A(13, 2) and point B(7, 10) is 10 units.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/08\/learnexams-banner5-309.jpeg\" alt=\"\" class=\"wp-image-280910\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: The correct answer is&nbsp;10. To find the distance between two points, A(13, 2) and B(7, 10), in a two-dimensional plane, we use the distance formula. This formula is derived from the Pythagorean theorem and is expressed as: d = \u221a[(x\u2082 &#8211; x\u2081)\u00b2 + (y\u2082 &#8211; y\u2081)\u00b2] Here, (x\u2081, y\u2081) [&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-280908","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/280908","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=280908"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/280908\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=280908"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=280908"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=280908"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}