To determine if there is a line of symmetry for the rectangle formed by the points A(8,5), R(8,-1), D(-2,-1), and W(-2,-5), let's first analyze the coordinates of the rectangle.
- The points A(8,5) and R(8,-1) are vertically aligned (same x-coordinate).
- The points D(-2,-1) and W(-2,-5) are also vertically aligned.
- The rectangle can be confirmed since opposite sides are parallel and equal in length.
To find a line of symmetry, we need to see if the rectangle can be folded over a line and result in both sides matching perfectly.
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x-axis: This line would reflect points A and R (top edge) to below the x-axis, and D and W (bottom edge) to above the x-axis, which does not maintain symmetry. So not a line of symmetry.
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x = 3: This line is positioned between the left and right edges of the rectangle (from x = -2 to x = 8). Reflecting points across x = 3 would not put them in their original positions since the distances from that line are unequal. So not a line of symmetry.
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y-axis: The points at A and R would reflect to (8,5) and (8,-1) on the opposite side of the y-axis, and D and W would change to (-2,-1) and (-2,-5) which do not match their original locations. So not a line of symmetry.
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y = 3: This line runs through the midpoint of the vertical height of the rectangle. The top edge (points A, R) would reflect down to points D and W respectively. Since the rectangle maintains a consistent distance from this line on both sides, it creates a perfect match.
Thus, the line of symmetry identified is:
D. y = 3