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 (0,0), (−8,0), (0,−6), and (−8,−6), we first analyze the positions of the vertices.

These points form a rectangle since the opposite sides are equal and parallel:

• The vertices (0, 0) and (−8, 0) are on the top side of the rectangle.
• The vertices (0, -6) and (−8, -6) are on the bottom side of the rectangle.

Now, to find the vertical line of symmetry, we need to ascertain the midpoint between the leftmost point (−8, 0) and the rightmost point (0, 0).

The x-coordinates of the leftmost point (−8) and the rightmost point (0) average as follows:

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

Thus, the vertical line of symmetry is given by the equation:

\[ x = -4 \]

So, the complete answer is:

x = -4.