Find the value of k for which the points A (-1, 3), B (2, k) and C (5…

The correct answer is Option (2) → 1

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

Points:

• A(-1, 3)
• B(2, k)
• C(5, -1)

Step 1: Slope of AC

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

Step 2: Slope of AB

$\text{slope } AB = \frac{k - 3}{2 - (-1)} = \frac{k - 3}{3}$

Step 3: Equate the slopes

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

$k - 3 = -2$

$k = 1$