Question

If the points A(x, 2), B(−3, −4) and C(7, −5) are collinear then the value of x is [CBSE 2014]
(a) −63 (b) 63 (c) 60 (d) −60

Answer 1

Let A(x₁ = x, y₁ = 2), B(x₂ = −3, y₂ = −4) and C(x₃ = 7, y₃ = −5) be collinear points. Then
$$\begin{gathered} x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)=0 \\ \Rightarrow x\left(-4+5\right)+\left(-3\right)\left(-5-2\right)+7\left(2+4\right)=0 \\ \Rightarrow x+21+42=0 \\ \Rightarrow x=-63 \end{gathered}$$
Hence, the correct answer is option (a).