In the diagram, the line segments $P Q$ and $P R$ are perpendicular. The value of $s$ is
(A) 6
(B) 9
(C) 10
(D) 12
(E) 9.5

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-027.jpg?height=504&width=444&top_left_y=1870&top_left_x=1293)
The slope of line segment $P R$ is $\frac{2-1}{0-4}$ which equals $-\frac{1}{4}$.

Since $\angle Q P R=90^{\circ}$, then $P Q$ and $P R$ are perpendicular.

This means that the slopes of $P Q$ and $P R$ have a product of -1 .

Since the slope of $P R$ is $-\frac{1}{4}$, then the slope of $P Q$ is 4 .

Since the "run" of $P Q$ is $2-0=2$, then the "rise" of $P Q$ must be $4 \times 2=8$.

Thus, $s-2=8$ and so $s=10$.

ANSWER: (C)