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

Solution (By Examveda Team)

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
$$\eqalign{ & \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} = \frac{{{y_3} - {y_2}}}{{{x_3} - {x_2}}} \cr & \frac{{4 + 2}}{{1 - 3}} = \frac{{x - 4}}{{ - 2 - 1}} \cr & \frac{6}{{ - 2}} = \frac{{x - 4}}{{ - 3}} \cr & 9 = x - 4 \cr & x = 13 \cr} $$