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