2004 AMC 12B Problems/Problem 9

Problem

The point $(-3,2)$ is rotated $90^\circ$ clockwise around the origin to point $B$ . Point $B$ is then reflected over the line $x=y$ to point $C$ . What are the coordinates of $C$ ?

$\mathrm{(A)}\ (-3,-2) \qquad \mathrm{(B)}\ (-2,-3) \qquad \mathrm{(C)}\ (2,-3) \qquad \mathrm{(D)}\ (2,3) \qquad \mathrm{(E)}\ (3,2)$

Solution

The entire situation is in the picture below. The correct answer is $\boxed{\mathrm{(E)}\ (3,2)}$ .

$[asy] unitsize(1cm); defaultpen(0.8); pair A=(-3,2), B=rotate(-90)*A, C=(3,2); dot(A); dot(B); dot(C); draw( A -- (0,0) -- B -- C, Dotted ); draw( (-3,-3) -- (4,4), dashed ); label("$A=(-3,2)$", A, NW ); label("$B=(2,3)$", B, N ); label("$C=(3,2)$", C, E ); label("$x=y$",(4,4),NE); dot((0,0)); label("$(0,0)$", (0,0), SE); [/asy]$

2004 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 8	Followed by Problem 10
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2004 AMC 12B Problems/Problem 9

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