Question

A quadrilateral has vertices (0,0)(0,0) , (−8,0)(−8,0) , (0,−6)(0,−6) and (−8,−6)(−8,−6) Complete the equation with the vertical line of symmetry that will carry the quadrilateral onto itself.(1 point)x=𝑥= is the vertical line of symmetry of the quadrilateral.

Answer 1

To find the vertical line of symmetry of the quadrilateral with vertices \( (0,0) \), \( (-8,0) \), \( (0,-6) \), and \( (-8,-6) \), we first plot the vertices and examine their arrangement.

The quadrilateral has the following coordinates:
- Top left: \( (0,0) \)
- Top right: \( (-8,0) \)
- Bottom left: \( (0,-6) \)
- Bottom right: \( (-8,-6) \)

This quadrilateral is a rectangle that spans horizontally from \( x = -8 \) to \( x = 0 \) and vertically from \( y = -6 \) to \( y = 0 \).

The line of symmetry for a rectangle oriented this way is located exactly halfway between the leftmost and rightmost points. The leftmost point is \( -8 \) and the rightmost point is \( 0 \).

To find the x-coordinate of the line of symmetry:
\[
\text{Line of symmetry} = \frac{-8 + 0}{2} = \frac{-8}{2} = -4
\]

Thus, the vertical line of symmetry is:
\[
x = -4
\]

Therefore, the answer is:
\[
x = -4
\]
This means the vertical line of symmetry that will carry the quadrilateral onto itself is \( x = -4 \).