Question

An image point after a 180° rotation is Z'(3, 7). What were the coordinates of the pre-image point?

Z(-3, -7)
Z(7, 3)
Z(-7, -3)
Z(7, -3)

Answer 1

Answer: Z(-3, -7)
The rule for 180 degree rotations is (x, y) -> (-x, -y). There is no change in the order of the coordinates; they just become negative. The pre-image point's coordinates are (-3, -7), because (-(-3), -(-7)) = (3, 7), which are the coordinates of Z'.