Problem:
A triangle with vertices , and is reflected about the axis; then the image is rotated counterclockwise around the origin by to produce . Which of the following transformations will return to ?
Answer Choices:
A. counterclockwise rotation around the origin by
B. clockwise rotation around the origin by
C. reflection about the -axis
D. reflection about the line
E. reflection about the -axis
Solution:
After reflection about the -axis, the coordinates of the image are , and . The counterclockwise -rotation around the origin maps this triangle to the triangle with vertices , and . Notice that the final image can be mapped to the original triangle by interchanging the - and -coordinates, which corresponds to a reflection about the line .
The problems on this page are the property of the MAA's American Mathematics Competitions