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

## See Also

 2004 AMC 12B (Problems • Answer Key • Resources) Preceded byProblem 8 Followed byProblem 10 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AMC 12 Problems and Solutions

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