Chapter 13.3, Problem 4WE

To determine

To find the slope $\overline{HI}$ , $\overline{JK}$ , $\overline{IJ}$ and $\overline{KH}$ of sides of rectangle $HIJK$ .

Answer to Problem 4WE

The slope $\overline{HI}$ and $\overline{JK}$ is $1$ , $\overline{IJ}$ and $\overline{KH}$ is $-1$

Explanation of Solution

Given:

Below is figure given

  

Calculation:

Slope of a line when two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ are given is

  $m=\frac{y_2-y_1}{x_2-x_1}$

points are $H\left(2,-5\right)\text{ and }B\left(6,-1\right)$

  $m_{HI}=\frac{-1-\left(-5\right)}{6-2}=1$

Since $HIJK$ is a rectangle

So, All the interior angles of rectangle are ${90}^{\circ }$ and opposite sides of rectangle are equal and parallel.

side $\overline{HI}$ is perpendicular to $\overline{IJ}$

  $\begin{array}{l}{m}_{HI}\times m_{IJ}=-1\\ 1\times m_{IJ}=-1\\ m_{IJ}=-1\end{array}$

  $\overline{HI}$ is parallel to $\overline{JK}$

So, $m_{HI}=m_{JK}=1$

  $\overline{IJ}$ is parallel to $\overline{KH}$

So, $m_{IJ}=m_{KH}=-1$

Therefore, the slope $\overline{HI}$ and $\overline{JK}$ is $1$ , $\overline{IJ}$ and $\overline{KH}$ is $-1$ .