{"id":18581,"date":"2025-06-13T07:38:24","date_gmt":"2025-06-13T07:38:24","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=18581"},"modified":"2025-06-13T07:38:26","modified_gmt":"2025-06-13T07:38:26","slug":"identify-the-true-statement","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/identify-the-true-statement\/","title":{"rendered":"Identify the true statement"},"content":{"rendered":"\n<p>Identify the true statement. A Nonparallel lines have the same slope. B Parallel lines have reciprocal slopes of opposite sign. C Perpendicular lines have the same slope. D Perpendicular lines have reciprocal slopes of opposite sign.<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p><strong>Correct Answer: D. Perpendicular lines have reciprocal slopes of opposite sign.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>To understand why <strong>option D<\/strong> is correct, we need to look at the properties of the slopes of lines in coordinate geometry.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>1. What is slope?<\/strong><\/h3>\n\n\n\n<p>The slope of a line measures its steepness and direction. It is calculated as: slope=riserun=y2\u2212y1x2\u2212x1\\text{slope} = \\frac{\\text{rise}}{\\text{run}} = \\frac{y_2 &#8211; y_1}{x_2 &#8211; x_1}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>2. Perpendicular Lines (Correct Answer D):<\/strong><\/h3>\n\n\n\n<p>Two lines are <strong>perpendicular<\/strong> if they intersect at a <strong>90-degree angle<\/strong>. The key property is:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Their slopes are <strong>negative reciprocals<\/strong> of each other.<\/li>\n<\/ul>\n\n\n\n<p>If one line has slope mm, then the other line has slope \u22121m-\\frac{1}{m}, assuming m\u22600m \\neq 0.<\/p>\n\n\n\n<p><strong>Example:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Line A has a slope of 2.<\/li>\n\n\n\n<li>Line B must then have a slope of \u221212-\\frac{1}{2} to be perpendicular to Line A.<\/li>\n<\/ul>\n\n\n\n<p>This relationship ensures the lines form a right angle when they intersect.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>3. Why the Other Options Are Incorrect:<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>A. Nonparallel lines have the same slope<\/strong><br>\u274c Incorrect. Lines with the same slope are <strong>parallel<\/strong>, not nonparallel.<\/li>\n\n\n\n<li><strong>B. Parallel lines have reciprocal slopes of opposite sign<\/strong><br>\u274c Incorrect. <strong>Parallel lines<\/strong> have <strong>equal slopes<\/strong>, not reciprocal or opposite.<\/li>\n\n\n\n<li><strong>C. Perpendicular lines have the same slope<\/strong><br>\u274c Incorrect. If lines have the same slope, they are <strong>parallel<\/strong>, not perpendicular.<\/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>Conclusion:<\/strong><\/h3>\n\n\n\n<p>The only true statement is <strong>D<\/strong>: <em>Perpendicular lines have reciprocal slopes of opposite sign<\/em>. This is a foundational concept in algebra and geometry and is often used when analyzing or constructing right angles between linear equations on a coordinate plane.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Identify the true statement. A Nonparallel lines have the same slope. B Parallel lines have reciprocal slopes of opposite sign. C Perpendicular lines have the same slope. D Perpendicular lines have reciprocal slopes of opposite sign. The correct answer and explanation is: Correct Answer: D. Perpendicular lines have reciprocal slopes of opposite sign. Explanation: To [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-18581","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18581","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=18581"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18581\/revisions"}],"predecessor-version":[{"id":18582,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18581\/revisions\/18582"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=18581"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=18581"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=18581"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}