Chapter 6.6, Problem 79SPR

To determine

The graph of each quadrilateral with given vertices and whether it is a rectangle using Slope Formula.

Answer to Problem 79SPR

  

JKLM is not a rectangle.

Explanation of Solution

Given:

The given vertices are:

  $J\left(0,7\right),K\left(-8,6\right),L(-7,0),M\left(1,1\right).$

Calculation:

Draw the quadrilateral using given vertices:

  

A rectangle is a parallelogram that has 4 right angles.

The slope of JK will be:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{6-7}{-8-0}\\ m=\frac{-1}{-8}\\ m=-\frac{1}{8}\end{array}$

The slope of KL will be:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{0-6}{-7-\left(-8\right)}\\ m=\frac{-6}{1}\\ m=-6\end{array}$

The slope of LM will be:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{1-0}{1-\left(-7\right)}\\ m=\frac{1}{8}\end{array}$

The slope of MJ will be:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{1-7}{1-0}\\ m=\frac{-6}{1}\\ m=-6\end{array}$

As, $\frac{1}{8}\left(-6\right)\ne -1,$ the consecutive sides of given figure are not perpendicular.

Therefore, JKLM is not a rectangle.