Question

reflect square ABCD with points A (3,-4); B (7, -4); C (7, -8) and D ( 3, -8) first across the x-axis, and then across the y-axis to create square A'B'C'D'. What are the vertices of the new square?

Answer 1

To reflect the square ABCD first across the x-axis and then across the y-axis, we can follow these steps:

1. **Reflect across the x-axis**: The reflection of a point \((x, y)\) across the x-axis is \((x, -y)\).

- A (3, -4) becomes A' (3, 4)
- B (7, -4) becomes B' (7, 4)
- C (7, -8) becomes C' (7, 8)
- D (3, -8) becomes D' (3, 8)

So after this step, the vertices are:
- A' (3, 4)
- B' (7, 4)
- C' (7, 8)
- D' (3, 8)

2. **Reflect across the y-axis**: The reflection of a point \((x, y)\) across the y-axis is \((-x, y)\).

- A' (3, 4) becomes A'' (-3, 4)
- B' (7, 4) becomes B'' (-7, 4)
- C' (7, 8) becomes C'' (-7, 8)
- D' (3, 8) becomes D'' (-3, 8)

After performing both reflections, the vertices of the new square A'B'C'D' are:
- A'' (-3, 4)
- B'' (-7, 4)
- C'' (-7, 8)
- D'' (-3, 8)

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