To solve this problem, we proceed with the following steps:

Step 1: Assign coordinates to the square

Let the square $ABCD$ be on the coordinate plane with:

• $A = (0, 0)$,
• $B = (18, 0)$,
• $C = (18, 18)$,
• $D = (0, 18)$.

Let $P = (x, 0)$ on segment $AB$, where $0 \leq x \leq 18$.

Step 2: Equations of lines

• Line $CP$: Slope is $\frac{18}{x - 18}$, so the equation of $CP$ is: $y - 0 = \frac{18}{x - 18} (x - 18) \quad \implies \quad y = \frac{18}{x - 18} (X - x).$