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The area of a triangle with vertices (a, b + c), (b, c + a) and (c, a + b) is

(A) (a + b + c) 2     

(B) 0  

(C) a + b + c  

(D) abc

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Question 21 The area of a triangle with vertices (a, b + c), (b, c + a) and (c, a + b) is (A) (a + b + c)2 (B) 0 (C) a + b + c (D) abc Given vertices (a, b + c), (b, c + a) and (c, a + b) Here x1 = a , y1 = b + c x2 = b , y2 = c + a x3 = c , y3 = a + b Now, Area of triangle = 1/2 [ x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2) ] = 1/2 [ a([c + a] – [a + b]) + b([a + b] – [b + c]) + c([b + c] – [c + a]) ] = 1/2 [ a(c − b) + b(a − c) + c(b − a) ] = 1/2 [ ac − ab + ab − bc + bc − ac] = 1/2 × 0 = 0 square units So, the correct answer is (B)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.