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