Reflect square ABCD with respect to the x-axis and the y-axis. What are the vertices of square A′B′C′D

Answer 1

To reflect square ABCD with respect to the x-axis, we change the sign of the y-coordinates of each vertex.

The vertices of square ABCD are A(1,1), B(1,-1), C(-1,-1), and D(-1,1).

Reflecting with respect to the x-axis:

A' = (1, -1)
B' = (1, 1)
C' = (-1, 1)
D' = (-1, -1)

To reflect square ABCD with respect to the y-axis, we change the sign of the x-coordinates of each vertex.

Reflecting with respect to the y-axis:

A' = (-1, 1)
B' = (-1, -1)
C' = (1, -1)
D' = (1, 1)

Therefore, the vertices of square A'B'C'D' after reflecting with respect to the x-axis are A' (1, -1), B' (1, 1), C' (-1, 1), and D' (-1, -1).

The vertices of square A'B'C'D' after reflecting with respect to the y-axis are A' (-1, 1), B' (-1, -1), C' (1, -1), and D' (1, 1).