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2004 AMC 12B Problem 9

Problem 9 of 25EasierGeometry

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

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Solution

Rotating (−3,2)(-3, 2) by 90∘90^\circ clockwise sends (x,y)→(y,−x),(x, y) \to (y, -x), giving B=(2,3).B = (2, 3). Reflecting in y=xy = x swaps coordinates, giving C=(3,2).C = (3, 2). Thus, the correct answer is E.
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Tagged: transformation · coordinate geometry

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