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)

Explanation:

Step1: Identify the shape

The quadrilateral has vertices \((0, 0)\), \((-8, 0)\), \((0, -6)\), and \((-8, -6)\). This is a rectangle (since opposite sides are equal and all angles are right angles).

Step2: Find the midpoint of the horizontal sides

For a vertical line of symmetry in a rectangle (or any figure with horizontal sides), the line of symmetry is the vertical line that passes through the midpoint of the horizontal sides. The horizontal sides are between \(x = 0\) and \(x=-8\). The midpoint formula for the x - coordinates is \(\frac{x_1 + x_2}{2}\). Here, \(x_1=0\) and \(x_2 = - 8\). So, \(\frac{0+(-8)}{2}=\frac{-8}{2}=-4\).

Step3: Determine the equation of the vertical line

A vertical line has the equation \(x = a\), where \(a\) is the x - coordinate of all points on the line. Since the midpoint has an x - coordinate of \(-4\), the equation of the vertical line of symmetry is \(x=-4\).

Answer:

\(x = - 4\)