Problem:
Which one of the following rigid transformations (isometries) maps the line segment onto the line segment so that the image of is and the image of is ?
Answer Choices:
A. reflection in the -axis
B. counterclockwise rotation around the origin by
C. translation by 3 units to the right and 5 units down
D. reflection in the -axis
E. clockwise rotation about the origin by 180^
Solution:
We can simply graph the points, or use coordinate geometry, to realize that both and are, respectively, obtained by rotating and by about the origin. Hence the rotation by about the origin maps the line segment to the line segment , so the answer is .
OR
Notice that the transformation is obtained by reflecting points across the origin. Only and involve the origin, and since obviously reflection across the origin is , the answer is .
The problems on this page are the property of the MAA's American Mathematics Competitions