Question

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

Answer 1

To find the vertical line of symmetry for the given quadrilateral with vertices at (0,0), (−8,0), (0,−6), and (−8,−6), we first identify the midpoints of opposite sides.

The horizontal vertices are (0,0) and (−8,0), while the midpoints can be calculated as follows:
1. The midpoint of the horizontal segment joining (0,0) and (−8,0) is:
\[
\left( \frac{0 + (-8)}{2}, \frac{0 + 0}{2} \right) = (-4, 0)
\]

2. The midpoint of the horizontal segment joining (0,−6) and (−8,−6) is:
\[
\left( \frac{0 + (-8)}{2}, \frac{-6 + (-6)}{2} \right) = (-4, -6)
\]

Thus, the midpoints of the top and bottom sides of the quadrilateral are both at x = -4.

Since both midpoints lie on the vertical line \( x = -4 \) and the quadrilateral is symmetric with respect to this line, this line serves as a vertical line of symmetry.

Therefore, the complete equation is:
\[
x = -4
\]

Thus, the answer is:
\[
x = -4 \text{ is the vertical line of symmetry of the quadrilateral.}
\]