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imc

geometry intermediate

Problem

A triangle with vertices , , and is reflected about the -axis, then the image is rotated counterclockwise about the origin by to produce . Which of the following transformations will return to ?
(A) counterclockwise rotation about the origin by .
(B) clockwise rotation about the origin by .
(C) reflection about the -axis
(D) reflection about the line
Solution
Consider a point . Reflecting it about the -axis will map it to , and rotating it counterclockwise about the origin by will map it to . The operation that undoes this is a reflection about the , so the answer is .
Final answer
D