Question

Complete the equations identifying both lines of symmetry for ABCD, A = (-5, 3), B = (1, 3), C = (-5, -1),, D = (1, -1)

Answer 1

To determine the lines of symmetry for the quadrilateral ABCD with the given vertices A = (-5, 3), B = (1, 3), C = (-5, -1), and D = (1, -1), we can perform the following analysis:

1. **Plot the Points**:
- A = (-5, 3)
- B = (1, 3)
- C = (-5, -1)
- D = (1, -1)

When plotted, these points form a rectangle. The vertices A and B are on the same horizontal line at y = 3, while vertices C and D are on the horizontal line at y = -1.

2. **Identifying Symmetries**:
- **Vertical Symmetry**: The line of symmetry vertically bisects the rectangle. This line passes through the midpoints of the horizontal sides AB and CD.
- The midpoint of A(-5, 3) and B(1, 3) is at x = (-5 + 1) / 2 = -2.
- Therefore, the line of symmetry is vertical: **x = -2**.

- **Horizontal Symmetry**: The line of symmetry horizontally bisects the rectangle and goes through the midpoints of the vertical sides AD and BC.
- The midpoint of A(-5, 3) and C(-5, -1) is at y = (3 + (-1)) / 2 = 1.
- Therefore, the line of symmetry is horizontal: **y = 1**.

3. **Conclusion**: The lines of symmetry for the rectangle ABCD are:
- Vertical line of symmetry at **x = -2**
- Horizontal line of symmetry at **y = 1**