Question

Which statement is true about figures ABCD and A′B′C′D′? A polygon ABCD has A at ordered pair 2, negative 2, B at 1, negative 4, C at 0 and negative 2, D at 1 and negative 1. A polygon A prime B prime C prime D prime has A prime at ordered pair negative 2, negative 2, B prime at ordered pair negative 1, negative 4, C prime at ordered pair 0, negative 2 and D prime at ordered pair negative 1, negative 1. A′B′C′D′ is obtained by rotating ABCD counterclockwise by 180 degrees about the origin and then reflecting it across the x-axis. A′B′C′D′ is obtained by translating ABCD 2 units up and then reflecting it about the y-axis. A′B′C′D′ is obtained by translating ABCD 2 units up and then reflecting it about the x-axis. A′B′C′D′ is obtained by rotating ABCD counterclockwise by 180 degrees about the origin and then reflecting it across the y-axis.

Answer 1

C

Explanation:

Answer 2

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'.