Chapter 4.3, Problem 20PPS

To determine

To find: the slope of the line joining the two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ given by the formula $m=\frac{y_2-y_1}{x_2-x_1}$ .

Answer to Problem 20PPS

The given two lines are neither parallel nor perpendicular to each other.

Explanation of Solution

Given information:

On a map, D drive passes through $R\left(0,-9\right)$ and $S\left(4,-11\right)$ , and L road passes through $J\left(4,-5\right)$ and $K\left(6,-2\right)$

Calculation:

The slope of the line $m_1$ joining the points $R\left(0,-9\right)$ and $S\left(4,-11\right)$ ,

Now,

  $\begin{array}{c}{m}_1=\frac{-11-(-9)}{4-0}\\ =-\frac{2}{4}\\ =-\frac{1}{2}\end{array}$

The slope of the line $m_2$ joining the points $J\left(4,-5\right)$ and $K\left(6,-2\right)$

  $\begin{array}{c}{m}_2=\frac{-2-(-5)}{6-4}\\ =\frac{3}{2}\end{array}$

Here $m_1$ is not equal to $m_2$ also $m_1$ is not negative reciprocal of $m_2$ .

Therefore, the given two lines are neither parallel nor perpendicular to each other.