If the points A (1, 2), O (0, 0) and C (a, b) are collinear, then

(A) a = b  

(B) a = 2b  

(C) 2a = b  

(D) a = –b

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Question 23 If the points A (1, 2), O (0, 0) and C (a, b) are collinear, then (A) a = b (B) a = 2b (C) 2a = b (D) a = –b Since points A, O, C are collinear, they will lie on the same line, i.e. they will not form triangle Therefore, Area of ∆AOC = 0 1/2 [ x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2) ] = 0 Here x1 = 1, y1 = 2 x2 = 0, y2 = 0 x3 = a, y3 = b Putting values 𝟏/𝟐 [ 1(0 – b) + 0(b − 2) + a(2 − 0) ] = 0 1 (−b) + 0 + 2a = 0 × 2 −b + 2a = 0 2a = b So, the correct answer is (C)

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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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.