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2009 CEMC Pascal Problems/Problem 7

Problem

In the diagram, $\triangle PQR$ is right-angled at $Q$, $PQ$ is horizontal and $QR$ is vertical. What are the coordinates of $Q$?

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$\text{ (A) }\ (5, 2) \qquad\text{ (B) }\ (5, 0) \qquad\text{ (C) }\ (5, 1) \qquad\text{ (D) }\ (4, 1) \qquad\text{ (E) }\ (1, 5)$

Solution

Since $PQ$ is horizontal and $QR$ is vertical, point $Q$ must have the same y-coordinate as point $P$ and the same x-coordinate as point $R$.

This works out to $\boxed {\textbf {(C) } (5, 1)}$.

~anabel.disher

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