What is the value of x for which the points A (-1, 3), B (2, x) and C (5, -1) are collinear?

1

The correct answer is Option (2) → 1

For three points to be collinear, the slopes between any two pairs must be equal.

Given points:

• $A(-1, 3)$
• $B(2, x)$
• $C(5, -1)$

Step 1: Slope of AC

$m_{AC} = \frac{-1 - 3}{5 - (-1)} = \frac{-4}{6} = -\frac{2}{3}$

Step 2: Slope of AB

$m_{AB} = \frac{x - 3}{2 - (-1)} = \frac{x - 3}{3}$​

Step 3: Set slopes equal

$\frac{x - 3}{3} = -\frac{2}{3}$

$x−3=−2$

$x=1$

Correct answer: 1