Chapter 4.3, Problem 20PPS

To determine

To find: Whether the two roads (streets) are perpendicular. Explain.

Answer to Problem 20PPS

The roads are perpendicular to each other.

Explanation of Solution

Given information: The two straight roads RS and JK passes through the points $R\left(4,-11\right),S\left(0,-9\right)\text{ and }J\left(6,-2\right),K\left(4,-5\right)$ .

Calculation: If $m_{RS}\text{ and }{m}_{JK}$ are slopes of roads RS and JK respectively, then these slopes are evaluated as,

  $\begin{array}{c}{m}_{RS}=\frac{-9+11}{0-4}\\ =-\frac{1}{2}\\ m_{JK}=\frac{-5+2}{4-6}\\ =\frac{3}{2}\end{array}$

Since, the slopes $m_{RS}\text{ and }{m}_{JK}$ are not negative reciprocal to one another. Therefore, the streets RS and JK are perpendicular to one another.