Question

Reflect square ABCD with respect to the x -axis and the y -axis. What are the vertices of square A′B′C′D′? (1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

When a point is reflected over the x-axis, the x-coordinate remains the same, but the y-coordinate changes sign.

When a point is reflected over the y-axis, the y-coordinate remains the same, but the x-coordinate changes sign.

So, let's consider the vertices of square ABCD: A, B, C, and D.

Reflecting square ABCD with respect to the x-axis:
- Vertex A remains the same since both the x-coordinate and y-coordinate do not change when reflected over the x-axis.
- Vertex B has its x-coordinate stay the same, but its y-coordinate changes sign. So, vertex B' is (x, -y).
- Vertex C has its x-coordinate stay the same, but its y-coordinate changes sign. So, vertex C' is (x, -y).
- Vertex D remains the same since both the x-coordinate and y-coordinate do not change when reflected over the x-axis.

Reflecting square ABCD with respect to the y-axis:
- Vertex A has its y-coordinate remain the same, but its x-coordinate changes sign. So, vertex A' is (-x, y).
- Vertex B has its y-coordinate remain the same, but its x-coordinate changes sign. So, vertex B' is (-x, y).
- Vertex C remains the same since both the x-coordinate and y-coordinate do not change when reflected over the y-axis.
- Vertex D has its y-coordinate remain the same, but its x-coordinate changes sign. So, vertex D' is (-x, y).

Therefore, the vertices of square A'B'C'D' are:
A' = (-x, y)
B' = (-x, -y)
C' = (x, -y)
D' = (x, y)