If the points X(2, -1), Y(3, k), Z(1, 4) are colinear, then the value…

The correct answer is Option (3) → -6

For points $X(2,−1), Y(3,k), Z(1,4)$ to be collinear, the slopes between any two pairs must be equal.

Step 1: Slope formula

$\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}$

Slope of $XY = \frac{k - (-1)}{3 - 2} = \frac{k + 1}{1} = k + 1$

Slope of $XZ = \frac{4 - (-1)}{1 - 2} = \frac{5}{-1} = -5$

Step 2: Equate slopes

$k + 1 = -5$

$k = -6$