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.
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 need to understand the shape and position of the quadrilateral.

The vertices can be identified as follows:
- (0, 0) is the top right vertex.
- (−8, 0) is the top left vertex.
- (0, −6) is the bottom right vertex.
- (−8, −6) is the bottom left vertex.

The quadrilateral is a rectangle because it has opposite sides that are equal and parallel.

To find the vertical line of symmetry, we look for a line that divides the rectangle into two equal halves. The symmetry line in this case can be determined by finding the midpoint along the horizontal axis between the leftmost and rightmost vertices.

The coordinates of the leftmost vertex are \((-8, 0)\), and the coordinates of the rightmost vertex are \((0, 0)\). The x-coordinate of the vertical line of symmetry can be calculated as:

\[
\text{Midpoint} = \frac{x_1 + x_2}{2} = \frac{-8 + 0}{2} = \frac{-8}{2} = -4
\]

Thus, the vertical line of symmetry is:

\[
x = -4
\]

Therefore, the complete equation is:

x = -4 is the vertical line of symmetry of the quadrilateral.