2004 AMC 12B Problem 9

Problem 9 of 25EasierGeometry

The point

(-3, 2)

is rotated

90^\circ

clockwise around the origin to point

B.

Point

B

is then reflected in the line

y = x

to point

C.

What are the coordinates of

C?

Show solution

Solution

Rotating

(-3, 2)

90^\circ

clockwise sends

(x, y) \to (y, -x),

giving

B = (2, 3).

Reflecting in

y = x

swaps coordinates, giving

C = (3, 2).

Thus, the correct answer is E.

Concepts: transformation · coordinate geometry

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.