Problem:
The point in the -plane is first rotated counterclockwise by around the point and then reflected about the line . The image of after these two transformations is at . What is ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Answer (D): The image of before the reflection about must have been ( ). The coordinates of can then be found by rotating this point clockwise by around the point . Because ( ) is 4 units to the left and 1 unit up from , the point must be 4 units up and 1 unit to the right from . Therefore the coordinates of must be , so .
The problems on this page are the property of the MAA's American Mathematics Competitions