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.

Question

x = _ is the vertical line of symmetry of the quadrilateral

Answer 1

To determine the vertical line of symmetry for the given quadrilateral with vertices at (0, 0), (-8, 0), (0, -6), and (-8, -6), we first analyze the positions of these vertices.

The quadrilateral is defined by the following points:

1. (0, 0)
2. (-8, 0)
3. (0, -6)
4. (-8, -6)

We can observe the following about the positions of the vertices:

• Points (0, 0) and (-8, 0) are horizontally aligned at \(y = 0\) along the x-axis.
• Points (0, -6) and (-8, -6) are also horizontally aligned at \(y = -6\).

Now, let's find the midpoint of the line segments between the points on the left (x = -8) and the points on the right (x = 0).

The coordinates from the left (-8) to the right (0) give us:

1. Midpoint between (0, 0) and (-8, 0): \[ \left(\frac{0 + (-8)}{2}, \frac{0 + 0}{2}\right) = \left(-4, 0\right) \]

2. Midpoint between (0, -6) and (-8, -6): \[ \left(\frac{0 + (-8)}{2}, \frac{-6 + (-6)}{2}\right) = \left(-4, -6\right) \]

From these midpoints, we see that both midpoints have the same x-coordinate of -4.

Thus, the vertical line of symmetry, which is a vertical line equidistant from both sides of the quadrilateral, is given by:

\[ x = -4 \]

So the answer is:

\[ x = -4 \]