Use the image to answer the question.

Rectangle upper W (-2,5) upper A (8,5) upper R (8,-1) upper D (-2,-1) is plotted on a coordinate plane.

Examine the polygon in the figure shown. Identify a line of symmetry that will flip the figure onto itself.

(1 point)
Responses

y=3
y equals 3

x=3
x equals 3

x-axis
x -axis

y-axis
y -axis

1 answer

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:

  1. A rectangle has two lines of symmetry: one that runs vertically through the center and one that runs horizontally through the center.
  2. The center of the rectangle is at the midpoint of both the x-values and y-values.
  3. 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