JAMIA 2026 — Mathematics PYQ

Step 1: Formula for the slope of a line

The slope ($m$) between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by:

$$m=\frac{y_2-y_1}{x_2-x_1}$$

Step 2: Calculate the Slope of line segment $AB$

Using points $A(0,k)$ and $B(-3,0)$:

$$\text{Slope of }AB=\frac{0-k}{-3-0}=\frac{-k}{-3}=\frac{k}{3}$$

Step 3: Calculate the Slope of line segment $BC$

Using points $B(-3,0)$ and $C(5,8)$:

$$\text{Slope of }BC=\frac{8-0}{5-(-3)}=\frac{8}{5+3}=\frac{8}{8}=1$$

Step 4: Equate the slopes to find $k$

Since the points are collinear:

$$\text{Slope of }AB=\text{Slope of }BC$$

$$\frac{k}{3}=1$$

Multiplying both sides by $3$:

$$k=3$$

Correct Answer

The correct option is (b) $3$.