Step 1 (Formula / Governing Law & Given Data): [0.25 Mark]

Three points $A(x_1, y_1)$, $B(x_2, y_2)$, and $C(x_3, y_3)$ are collinear if the slope of line segment $AB$ is equal to the slope of line segment $BC$. Alternatively, the area of the triangle formed by these points must be zero.

Using the slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Given points: $A(2, 3)$, $B(0, 4)$, and $C(p, 2)$.

Step 2 (Step-by-Step Mathematical Working): [0.5 Mark]

Calculate the slope of $AB$ ($m_{AB}$):

$$m_{AB} = \frac{4 - 3}{0 - 2} = \frac{1}{-2} = -\frac{1}{2}$$

Calculate the slope of $BC$ ($m_{BC}$):

$$m_{BC} = \frac{2 - 4}{p - 0} = \frac{-2}{p}$$

Since the points are collinear, $m_{AB} = m_{BC}$:

$$-\frac{1}{2} = \frac{-2}{p}$$

Cross-multiplying to solve for $p$:

$$-p = -4 \implies p = 4$$

Step 3 (Final Concluded Answer): [0.25 Mark]

The value of $p$ is 4. Therefore, the correct option is (C).

💡 EL10 Concept Insight: Imagine the points are beads on a single straight string; if you tilt the string to connect the first two beads, the third bead must lie on that exact same tilt, meaning the "steepness" (slope) between any two pairs of beads must be identical.