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
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