Chapter 6.4, Problem 8CYU

To determine

The graph of each quadrilateral with given vertices and whether the figure forms a rectangle or not using slope formula.

Answer to Problem 8CYU

WXYZ is not a rectangle.

Explanation of Solution

Given:

The given vertices are:

  $W\left(-4,3\right),X\left(1,5\right),Y\left(3,1\right),Z\left(-2,-2\right).$

Calculation:

A rectangle is a parallelogram with 4 right angles.

The quadrilateral with given vertices will be:

The slope of line segment WZ will be:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{5-3}{1-\left(-5\right)}\\ m=\frac{2}{5}\end{array}$

The slope of line segment YZ will be:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{-2-1}{-2-3}\\ m=\frac{-3}{-5}\\ m=\frac{3}{5}\end{array}$

The slope of line WX is not equal to the slope of line YZ, hence it is not a parallelogram.

Therefore, WXYZ is not a rectangle.