{"id":4989,"date":"2012-11-30T03:01:37","date_gmt":"2012-11-30T03:01:37","guid":{"rendered":"http:\/\/SchoolTutoring.com\/help\/?p=4989"},"modified":"2014-12-02T08:31:56","modified_gmt":"2014-12-02T08:31:56","slug":"distance-between-two-parallel-lines","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/distance-between-two-parallel-lines\/","title":{"rendered":"Distance Between Two Parallel Lines"},"content":{"rendered":"<p>We know that the perpendicular distance from origin to a straight line whose equation is a+by+c=0 is |c|\/\u221a(a<sup>2<\/sup>+b<sup>2<\/sup>). Also, we know that the perpendicular distance from (h,k) to ax+by+c=0 is, |ah+bk+c|\/\u221a(a<sup>2<\/sup>+b<sup>2<\/sup>). These two are the formulas to find out the distances to a line from origin or a point. But, how to find the distances between two parallel lines? Let us derive the formula for the distance between two parallel lines.<\/p>\n<p>The general form of equation of a straight line is ax+by+c=0 whose slope is \u2013a\/b.<\/p>\n<p>We know the fact that any two lines are parallel if they have same slope. Thus, any two parallel lines have same coefficients of x and y but differs in constants.<\/p>\n<p>Let ax+by + p =0 and ax+by + q =0 be two parallel lines and let us find the distance between these lines now.<\/p>\n<p>Let (h,k) be a point of the line ax+by+p=0<\/p>\n<p><a href=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/2\/2012\/11\/parallel.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-4990\" title=\"parallel\" src=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/2\/2012\/11\/parallel.jpg\" alt=\"\" width=\"267\" height=\"191\" \/><\/a><\/p>\n<p>Then ah+bk +p=0 \u00e0 ah+bk =-p \u2026(1)<\/p>\n<p>Now distance from (h,k) to the second line ax+by +q=0 according to formula is,<\/p>\n<p>|ah+bk+q|\/\u221a(a<sup>2<\/sup>+b<sup>2<\/sup>)<\/p>\n<p>=|-p+q |\/\u221a(a<sup>2<\/sup>+b<sup>2<\/sup>) (By using equation (1))<\/p>\n<p>=|p-q |\/\u221a(a<sup>2<\/sup>+b<sup>2<\/sup>)<\/p>\n<p>Thanks for reading this Mathematics tutorial and remember we can help you with your <a href=\"https:\/\/schooltutoring.com\/tutoring-programs\/language-instruction\/french-tutoring\/\">French tutoring.<\/a><\/p>\n<p>SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Saskatchewan visit: <a href=\"https:\/\/schooltutoring.com\/Saskatchewan-Tutoring-Programs\/\">Tutoring in Saskatchewan. <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We know that the perpendicular distance from origin to a straight line whose equation is a+by+c=0 is |c|\/\u221a(a2+b2). Also, we know that the perpendicular distance from (h,k) to ax+by+c=0 is, |ah+bk+c|\/\u221a(a2+b2). These two are the formulas to find out the distances to a line from origin or a point. But, how to find the distances [&hellip;]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[10],"tags":[515,1280,1319,1662],"class_list":["post-4989","post","type-post","status-publish","format-standard","hentry","category-geometry","tag-distance","tag-parallel","tag-perpendicular","tag-slopes"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/4989","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=4989"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/4989\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=4989"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=4989"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=4989"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}