To identify a line of symmetry for the rectangle WARDE with vertices W (-2,5), A (8,5), R (8,-1), and D (-2,-1), we can analyze the structure of the rectangle:
- A rectangle has two lines of symmetry: one that runs vertically through the center and one that runs horizontally through the center.
- The center of the rectangle is at the midpoint of both the x-values and y-values.
- The x-coordinates of W and D are both -2 (left side) and A and R are both 8 (right side), indicating that the rectangle is symmetric about the vertical line halfway between -2 and 8.
Calculating the x-coordinate of the line of symmetry:
- Midpoint of x-coordinates: \((-2 + 8)/2 = 3\).
For the y-coordinate:
- The y-coordinates of W and A are both 5 (top side) and R and D are both -1 (bottom side), indicating symmetry about the horizontal line halfway between 5 and -1.
Calculating the y-coordinate of the line of symmetry:
- Midpoint of y-coordinates: \((5 + (-1))/2 = 2\).
Thus, the lines of symmetry are:
- \(x = 3\) (vertical line)
- \(y = 2\) (horizontal line)
Among the provided options focusing on the given rectangle's orientation and standard axes, the correct answer for a line that will flip the rectangle onto itself is:
x = 3