Answer:
A. a clockwise rotation around the origin followed by a translation of 5 units left and 2 units down
Step-by-step explanation:
You can check that a is correct by following these transformations by yourself. First there was a 90° rotation around the origin, so the points underwent this transformation (clockwise means (x, y) to (y, -x):
(-4, 2) --> (2, 4)
(-6, 2) --> (2, 6)
(-4, 7) --> (7, 4)
(-8, 7) --> (7, 8)
Now, you can just see if a translation left 5 and down 2 on one of the points would match it to its corresponding point. For example, I'll use (2, 4):
the corresponding corner to (2, 4) is (-3, 2)
(2 - 5, 4 - 2) = (-3, 2)?
(-3, 2) = (-3, 2)
Since the translation mapped it onto the correct point, you know that A is the correct answer.
