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 \( x = -4 \).
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