Use the image to answer the question.

Question

A quadrilateral on the coordinate plane.

Image Long DescriptionThe horizontal axis ranges from negative 8 to 2. The vertical axis ranges from negative 8 to 2. The vertices of the quadrilateral are as follows: 0 comma 0, negative 8 comma 0, 0 comma negative 6 and negative 8 comma negative 6.

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, we need to determine which x-coordinate would create a mirror effect that reflects the shape onto itself.

The vertices of the quadrilateral are:

• (0, 0)
• (−8, 0)
• (0, −6)
• (−8, −6)

The quadrilateral is symmetric around the vertical line that lies midway between the leftmost and rightmost points.

The leftmost point is at \( x = -8 \) and the rightmost point is at \( x = 0 \). The midpoint (which acts as the line of symmetry) can be calculated as follows:

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

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

\[ x = -4. \]

So, the complete answer is:

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