Question

examine the polygon in the figure shown. identify a line of symmetry that will flip the figure onto itself. (1 point)
○ ( y = 3 )
○ ( x )-axis
○ ( x = 3 )
○ ( y )-axis

Explanation:

Step1: Find coordinates of vertices

First, identify the coordinates of the vertices \( W(-2, 5) \), \( A(8, 5) \), \( R(8, -1) \), \( D(-2, -1) \).

Step2: Analyze midpoint of horizontal sides

The horizontal sides are \( WA \) (from \( x=-2 \) to \( x=8 \)) and \( DR \) (from \( x=-2 \) to \( x=8 \)). The midpoint of the \( x \)-coordinates: \( \frac{-2 + 8}{2} = \frac{6}{2} = 3 \). So the vertical line \( x = 3 \) will be the line of symmetry, as it is equidistant from \( x=-2 \) and \( x=8 \), and the \( y \)-coordinates for \( W \) and \( A \) are the same, \( D \) and \( R \) are the same. Checking other options: \( y=3 \) doesn't align, \( x \)-axis (\( y=0 \)) doesn't, \( y \)-axis (\( x=0 \)) doesn't.

Answer:

\( x = 3 \) (corresponding option: \( \boldsymbol{x = 3} \))