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)

Answer 1

To find the vertical line of symmetry for the given quadrilateral with vertices (0,0), (−8,0), (0,−6), and (−8,−6), we start by observing the arrangement of the vertices.

The quadrilateral has the following characteristics:
- The vertices (0,0) and (−8,0) are on the same horizontal line (y = 0).
- The vertices (0,−6) and (−8,−6) are on the same horizontal line (y = −6).
- All the points have the same x-coordinate (−8) offset from (0,0).

From this observation, we see that the quadrilateral is symmetric about a vertical line. Since the quadrilateral is bounded horizontally by \( x = 0 \) and \( x = -8 \), the line that is halfway between these two lines can be found by calculating the average of the x-coordinates:

\[
\text{Midpoint} = \frac{0 + (-8)}{2} = \frac{-8}{2} = -4
\]

Therefore, the vertical line of symmetry is:

\[
x = -4
\]

This line carries the quadrilateral onto itself, reflecting points across it. Hence, the complete answer is:

**x = -4**