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. (1 point) x = is the vertical line of symmetry of the quadrilateral.

Explanation:

Step1: Find the mid - point of horizontal side

For a rectangle (the given quadrilateral is a rectangle), the vertical line of symmetry passes through the mid - point of the horizontal sides. The horizontal side has endpoints with x - coordinates \(x_1 = 0\) and \(x_2=-8\).

Step2: Calculate the x - coordinate of the mid - point

The formula for the mid - point of two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(x=\frac{x_1 + x_2}{2}\). Substituting \(x_1 = 0\) and \(x_2=-8\) into the formula, we get \(x=\frac{0+( - 8)}{2}=\frac{-8}{2}=-4\).

Answer:

\(x = - 4\)