Question

Reflect rectangle ABCD across the y-axis, and then the x-axis. What are the vertices of
A'B'C'D'?

Answer 1

To reflect a shape across the y-axis, we need to change the sign of the x-coordinates of all the vertices.

Given rectangle ABCD, with vertices A = (a, b), B = (c, d), C = (e, f), and D = (g, h), when we reflect across the y-axis, the x-coordinates change sign:

A' = (-a, b)
B' = (-c, d)
C' = (-e, f)
D' = (-g, h)

To reflect A'B'C'D' across the x-axis, we need to change the sign of the y-coordinates of all the vertices:

A" = (-a, -b)
B" = (-c, -d)
C" = (-e, -f)
D" = (-g, -h)

Therefore, the vertices of A'B'C'D' are A" = (-a, -b), B" = (-c, -d), C" = (-e, -f), and D" = (-g, -h).