Chapter 6.4, Problem 22PPS

To determine

The graph of each quadrilateral with given vertices.

Answer to Problem 22PPS

It is a rectangle.

Explanation of Solution

Given:

The vertices are:

  $W\left(-2,4\right),X\left(5,5\right),Y\left(6,-2\right),Z\left(-1,-3\right)$

Calculation:

The graph will be:

The opposite sides of a parallelogram are congruent.

A rectangle has four right angles.

The slope of WX is:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{5-4}{5-\left(-2\right)}\\ m=\frac{1}{7}\end{array}$

The slope of XY is:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{-2-5}{6-5}\\ m=\frac{-7}{1}\\ m=-7\end{array}$

The slope of YZ is:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{-3-\left(-2\right)}{-1-6}\\ m=\frac{1}{7}\end{array}$

The slope of ZW is:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{4-\left(-3\right)}{-2-\left(-1\right)}\\ m=\frac{7}{-1}\\ m=-7\end{array}$

As, $-7\left(\frac{1}{7}\right)=-1,$ the adjacent sides of the given figure are perpendicular.

Hence, it is a rectangle.