Use the image to answer the question.

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 which only one answer is the correct perfect one and why

y=3
y equals 3

x=3
x equals 3

x-axis
x -axis

y-axis
y -axis

Answer 1

To determine the line of symmetry for the rectangle WARD, we can analyze its orientation on the coordinate plane. The rectangle's vertices are at (-2, 5), (8, 5), (8, -1), and (-2, -1).

1. Horizontal line of symmetry: A horizontal line has the equation \( y = k \). The horizontal midpoint of the rectangle is \( y = \frac{5 + (-1)}{2} = 2 \). The line \( y = 3 \) might seem like a candidate, but it does not actually bisect the rectangle into two equal halves.

2. Vertical line of symmetry: A vertical line has the equation \( x = k \). The vertical midpoint of the rectangle is \( x = \frac{-2 + 8}{2} = 3 \). The line \( x = 3 \) will equally split the rectangle into two identical halves.

3. x-axis and y-axis: While the rectangle does touch the x-axis and is symmetric relative to it, the x-axis is not the exact line of symmetry for this rectangle. The y-axis similarly does not bisect the rectangle into symmetry because the rectangle is asymmetrically placed around the y-axis.

Therefore, the correct line of symmetry that will flip the rectangle WARD onto itself is:

x = 3.

This line effectively bisects the rectangle vertically into two congruent halves.