To determine a line of symmetry for the given polygon with vertices W(-2,5), A(8,5), D(-2,-1), and R(8,-1), we can first analyze the coordinates of the points.
- Vertex W(-2,5) and A(8,5): These points are on the same horizontal line (y=5).
- Vertex D(-2,-1) and R(8,-1): These points are also on the same horizontal line (y=-1).
The polygon is therefore a rectangle with the top edge along the line y=5 (between W and A) and the bottom edge along the line y=-1 (between D and R).
Now let's examine the symmetries:
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Y-axis: This symmetry would reflect points across the y-axis. Points W and D would map to points with x-coordinates of +2 and +2 (not symmetric), while A and R would map to -8 and -8 (again not symmetric).
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Y=3: This line is only two units above the midpoint of the rectangle's height (which is between y=5 and y=-1). It does not equally divide the figure.
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X-axis: This line would reflect points across the x-axis. Since our figure does not cross through the x-axis, this would not be a line of symmetry.
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X=3: This is the middle of the rectangle since W and D (inputting x=-2 and x=8) go from -2 to 8, making the middle x=3. Reflecting W and A over this axis would map them to equal distances across the line.
Therefore, the line of symmetry that will flip the figure onto itself is X=3.
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