Abul Koderma, India 97 Questions 323 Answers 94 Best Answers 347 Points View Profile 24 AbulProficient Asked: October 22, 20202020-10-22T11:34:36+00:00 2020-10-22T11:34:36+00:00In: Maths Prove that the points (a, b+c), (b, c+a) and (c, a+b) are collinear. 24 Prove that the points (a, b+c), (b, c+a) and (c, a+b) are collinear. question Share Facebook 1 Answer Voted Oldest Recent Shrestha India 27 Questions 41 Answers 19 Best Answers 1,388 Points View Profile Best Answer Shrestha Guru 2021-05-04T08:45:54+00:00Added an answer on May 4, 2021 at 8:45 am Let the points be P(a, b+c), Q(b, c+a), and R(c, a+b). ar(∆PQR) = [x1(y2 – y3) + x2( y3 – y1)+ x3(y1 – y2)] ⇒ar(∆PQR) = [a(c + a – a – b) + b(a + b – b – c) + c(b + c – c – a)] ⇒ar(∆PQR) = [a(c – b) + b(a – c) + c(b – a)] ⇒ar(∆PQR) = [ac – ab + ab – bc + bc – ac] ⇒ar(∆PQR) = 0 Since, the area of triangle formed by the points P, Q and R is 0. So, points P, Q and R are collinear. 1 Share Share Share on Facebook Share on Twitter Share on LinkedIn Share on WhatsApp You must login to add an answer. Username or email* Password* Remember Me! Forgot Password?