Question

Square ABCD A (3, -4) B(7, -4) C(7, -8) D(3, -8)
Reflect square ABCD first across the a-axis, and then across the y-axis to create square A' B'C' D'. What are the vertices of square A' B'C' D'?

Answer 1

To find the vertices of square ABCD after reflecting it first across the x-axis and then the y-axis, we will perform each reflection step by step.

1. **Original Vertices of Square ABCD:**
- A (3, -4)
- B (7, -4)
- C (7, -8)
- D (3, -8)

2. **Reflection Across the x-axis:**
- To reflect a point (x, y) across the x-axis, we change the sign of the y-coordinate: (x, y) becomes (x, -y).
- Reflecting each vertex:
- A (3, -4) → A' (3, 4)
- B (7, -4) → B' (7, 4)
- C (7, -8) → C' (7, 8)
- D (3, -8) → D' (3, 8)

After the reflection across the x-axis, the new vertices are:
- A' (3, 4)
- B' (7, 4)
- C' (7, 8)
- D' (3, 8)

3. **Reflection Across the y-axis:**
- To reflect a point (x, y) across the y-axis, we change the sign of the x-coordinate: (x, y) becomes (-x, y).
- Reflecting each vertex from the previous step:
- A' (3, 4) → A'' (-3, 4)
- B' (7, 4) → B'' (-7, 4)
- C' (7, 8) → C'' (-7, 8)
- D' (3, 8) → D'' (-3, 8)

After reflection across the y-axis, the new vertices are:
- A'' (-3, 4)
- B'' (-7, 4)
- C'' (-7, 8)
- D'' (-3, 8)

Thus, the coordinates of the vertices of square A'B'C'D' are:
- A'' (-3, 4)
- B'' (-7, 4)
- C'' (-7, 8)
- D'' (-3, 8)