{"id":4994,"date":"2012-12-07T00:45:41","date_gmt":"2012-12-07T00:45:41","guid":{"rendered":"http:\/\/SchoolTutoring.com\/help\/?p=4994"},"modified":"2014-12-02T08:27:06","modified_gmt":"2014-12-02T08:27:06","slug":"what-is-the-foot-of-a-perpendicular","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/what-is-the-foot-of-a-perpendicular\/","title":{"rendered":"What is the “Foot of a Perpendicular”?"},"content":{"rendered":"

Let ax+by+c=0 be a straight line. If a perpendicular line \u00a0is drawn from any point on the plane to this straight line then the\u00a0 point of intersection of the given straight line and its perpendicular is called the foot of the corresponding perpendicular. \u00a0But how to find the coordinates of the foot of the perpendicular drawn from a point to the given line? Let us derive the formula now.<\/p>\n

Let ax+by+c=0 be the equation of straight line and assume that a perpendicular is drawn from a point (p,q) to this line and let the corresponding foot of the perpendicular be (h,k).<\/p>\n

\"\"<\/a><\/p>\n

The slope of perpendicular line joining (p,q) and (h,k) is k-q\/h-p<\/p>\n

The slope of line ax+by+c=0 is \u2013a\/b.<\/p>\n

Since the product of slopes of two perpendicular lines is -1,<\/p>\n

k-q\/h-p * -a\/b = -1<\/p>\n

h-p\/a = k-q\/b = m (say)<\/p>\n

h-p\/a = m and k-q\/b = m<\/p>\n

h = am+p\u00a0 and k = bm +q<\/p>\n

Since (h,k) is a point on the straight line ax+by+c=0 we have<\/p>\n

Ah+bk+c=0<\/p>\n

a(am+p) + b(bm+q) + c=0<\/p>\n

a2<\/sup>m+b2<\/sup>m + (ap+bq+c)=0<\/p>\n

m = -(ap+bq+c)\/(a2<\/sup>+b2<\/sup>)<\/p>\n

Thus the formula for finding the foot of the perpendicular is,<\/p>\n

h-p\/a = k-q\/b =-(ap+bq+c)\/(a2<\/sup>+b2<\/sup>)<\/em><\/strong><\/p>\n

Tutors for Study Skills<\/a> are also available if you need more help.<\/p>\n

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 Bainbridge visit: Tutoring in Bainbridge, WA. <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Let ax+by+c=0 be a straight line. If a perpendicular line \u00a0is drawn from any point on the plane to this straight line then the\u00a0 point of intersection of the given straight line and its perpendicular is called the foot of the corresponding perpendicular. \u00a0But how to find the coordinates of the foot of the perpendicular […]<\/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":[675,683,1319,1334],"class_list":["post-4994","post","type-post","status-publish","format-standard","hentry","category-geometry","tag-foot","tag-formula","tag-perpendicular","tag-plane"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/4994","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=4994"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/4994\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=4994"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=4994"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=4994"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}