Chapter 12, Problem 31CCSR

To determine

Find the slope of line that is perpendicular to line $p$ .

Answer to Problem 31CCSR

  $\frac{3}{11}$

Explanation of Solution

Given information:

Line $p$ passes through points, $\left(5,-4\right)and\left(2,7\right)$

Calculation:

Consider line $p$ passes through points, $\left(5,-4\right)and\left(2,7\right)$ is as drawn,

  

Slope of line $p$ is,

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}po\mathrm{int}s\left(5,-4\right),\left(2,7\right)\\ m_p=\frac{7-\left(-4\right)}{2-5}\\ =-\frac{11}{3}\end{array}$

Now find the slope of line $q$ which is perpendicular to $p$ is, if two lines are perpendicular to each other then slope will be,

  $\begin{array}{l}{m}_p\times m_q=-1\\ m_q=\frac{-1}{m_p}=\frac{-1}{-\frac{11}{3}}\\ m_q=\frac{3}{11}\end{array}$

Hence, slope of line that is perpendicular to line $p$ is $\frac{3}{11}$ .