If A (x, 2), B (−3, −4), and C (7, −5) are collinear, then the value of x is

(A) −63 

(B) 63

(C) 60 

(D) −60

This question is similar to Ex 7.3, 2 (i) - Chapter 7 Class 10 Coordinate Geometry

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Question 6 If A (x, 2), B (−3, −4), and C (7, −5) are collinear, then the value of x is (A) −63 (B) 63 (C) 60 (D) −60 Since points A, B, C are collinear, they will lie on the same line, i.e. they will not form triangle Therefore, Area of ∆ABC = 0 1/2 [ x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2) ] = 0 Here x1 = x, y1 = 2 x2 = - 3, y2 = - 4 x3 = 7, y3 = - 5 Putting values 𝟏/𝟐 [ x((−𝟒) – (−𝟓)) + (−𝟑)((−𝟓) − 2) + 𝟕(2 − (−𝟒)) ] = 0 𝑥 (−4 + 5) + (−3)(−7) + 7 (2+4) = 0 × 2 𝑥×1 + (−3)×(−7) + 7×6 = 0 𝑥 + 21 + 42 = 0 𝑥+63=0 𝒙=−𝟔𝟑 So, the correct answer is (A)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.