{"id":4971,"date":"2012-11-20T23:19:54","date_gmt":"2012-11-20T23:19:54","guid":{"rendered":"http:\/\/SchoolTutoring.com\/help\/?p=4971"},"modified":"2014-12-02T08:31:56","modified_gmt":"2014-12-02T08:31:56","slug":"geometry-distance-from-a-point-to-a-line","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/geometry-distance-from-a-point-to-a-line\/","title":{"rendered":"Geometry: Distance From a Point to a Line"},"content":{"rendered":"<p><strong>Distance from a point to a line:<\/strong><\/p>\n<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>). This formula works to find out the distance of a line from the origin whose coordinates are (0,0). Then how can we find the distance from a point different from origin to a given line? Let us see how we can find.<\/p>\n<p>Let (h,k) be a point and the equation of line be ax+by+c=0. Let us find the distance now.<\/p>\n<p>Let (x,y) be a point on the given line ax+by+c=0.<\/p>\n<p>For finding the distance, let us shift the origin from (0,0) to (h,k) as shown below.<\/p>\n<p><a href=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/2\/2012\/11\/distance-from-a-point-to-a-line.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-4972\" title=\"distance from a point to a line\" src=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/2\/2012\/11\/distance-from-a-point-to-a-line.jpg\" alt=\"\" width=\"278\" height=\"225\" \/><\/a><\/p>\n<p>Let the coordinates of (x,y) with respect to the new axes would be (X,Y). Then,<\/p>\n<p>x = X+h and y = Y+k<\/p>\n<p>Substituting these values into the given equation, we get<\/p>\n<p>a(X+h) + b(Y+k) + c =0<\/p>\n<p>aX + bY + (ah+bk+c)=0<\/p>\n<p>Since 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>), we have<\/p>\n<p><strong>The perpendicular distance from (h,k) to ax+by+c=0 is, |ah+bk+c|\/\u221a(a<sup>2<\/sup>+b<sup>2<\/sup>).<\/strong><\/p>\n<p>Thanks for reading this Math tutorial and remember we can also help you with your <a href=\"https:\/\/schooltutoring.com\/tutoring-programs\/private-tutoring\/\">Geography tutoring.<\/a><\/p>\n<p><span class=\"tutorOrange\">SchoolTutoring Academy<\/span> 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 Newfoundland visit: <a href=\"https:\/\/schooltutoring.com\/Newfoundland-Tutoring-Programs\/\">Tutoring in Newfoundland. <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Distance from a point to a line: We know that the perpendicular distance from origin to a straight line whose equation is a+by+c=0 is |c|\/\u221a(a2+b2). This formula works to find out the distance of a line from the origin whose coordinates are (0,0). Then how can we find the distance from a point different from [&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":[256,515,1039,1265,1319,1347],"class_list":["post-4971","post","type-post","status-publish","format-standard","hentry","category-geometry","tag-change-of-origin","tag-distance","tag-line","tag-origin","tag-perpendicular","tag-point"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/4971","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=4971"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/4971\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=4971"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=4971"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=4971"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}