Answer:
Step-by-step explanation:
A'B'C'D' is obtained by rotating ABCD 180° counterclockwise about the origin and then reflecting it across the x-axis.
A(2, -2) is mapped to A'(-2, -2)
B(1, -4) is mapped to B'(-1, -4)
C(0, -2) is mapped to C'(0, -2)
D(1, -1) is mapped to D'(-1, -1)
If we rotate counterclockwise 180°, every point (x, y) is mapped to (-x, -y):
A(2, -2) gets mapped to (-2, 2)
B(1, -4) gets mapped to (-1, 4)
C(0, -2) gets mapped to (0, 2)
D(1, -1) gets mapped to (-1, 1)
Reflecting these images across the x-axis will then map (x, y) to (x, -y):
(-2, 2) gets mapped to (-2, -2)
(-1, 4) gets mapped to (-1, -4)
(0, 2) gets mapped to (0, -2)
(-1, 1) gets mapped to (-1, -1)
These new coordinates are the same as A'B'C'D'.
