The points A(3, -2), B(1, 4) and C(-2, x) are collinear. What is the value of x?

Answer: Option A

A(3, -2), B(1, 4), C(-2, x)
Condition for collinearity of three points
0 = x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)
0 = 3(4 - x) + 1(x + 2) + (-2)(-2 - 4)
0 = 12 - 3x + x + 2 + 12
2x = 26
x = 13

Alternate Solution:
For collinear condition slope will be same
$$\begin{array}{rl}& \frac{y_2-y_1}{x_2-x_1}=\frac{y_3-y_2}{x_3-x_2}\\ & \frac{4+2}{1-3}=\frac{x-4}{-2-1}\\ & \frac{6}{-2}=\frac{x-4}{-3}\\ & 9=x-4\\ & x=13\end{array}$$