Question

Square has vertices A (2,4), B (2,11), C (7,11), and D (7,4). The square ABCD is
reflected on the x-axis and the y-axis. Find the
coordinates of the vertices for square A'B'C'D'.
Choose 1 for Option A and 2 for Option B.
Option A: Square A'B'C'D' has vertices A' (-2, -4), B' (-2, -11), C' (-7, -11), and D' (-7, -4).
Option B: Square A'B'C'D' has vertices A' (2, -4), B' (2, -11), C' (7, -11), and D' (7, -4). (1 point)

Answer 1

To find the coordinates of the vertices after reflecting the square ABCD across the x-axis and then the y-axis, we follow these steps:

1. **Reflection across the x-axis:** The x-coordinate remains the same, while the y-coordinate changes sign.
- A (2, 4) becomes A' (2, -4)
- B (2, 11) becomes B' (2, -11)
- C (7, 11) becomes C' (7, -11)
- D (7, 4) becomes D' (7, -4)

2. **Reflection across the y-axis:** The y-coordinate remains the same, while the x-coordinate changes sign.
- A' (2, -4) becomes A'' (-2, -4)
- B' (2, -11) becomes B'' (-2, -11)
- C' (7, -11) becomes C'' (-7, -11)
- D' (7, -4) becomes D'' (-7, -4)

So, the final coordinates after both reflections are:
- A'' (-2, -4)
- B'' (-2, -11)
- C'' (-7, -11)
- D'' (-7, -4)

Thus, the reflection results in:

**Option A:** Square A'B'C'D' has vertices A' (-2, -4), B' (-2, -11), C' (-7, -11), and D' (-7, -4).

So the correct option is **1 (Option A).**