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)

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.

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