Question

Examine the polygon in the figure shown. Identify a line of symmetry that will flip the figure onto itself. W(-2,5) A(8,5) D(-2,-1) R(8,-1)

Answer choices are:
y axis
Y=3
X-axis
X=3

Answer 1

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.

1. **Vertex W(-2,5) and A(8,5)**: These points are on the same horizontal line (y=5).
2. **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:

- **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).

- **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.

- **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.

- **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**.