# What is the slope of any line perpendicular to the line passing through (-21,2) and (-32,5)?

Dec 16, 2015

slope of the perpendicular line $= \frac{11}{3}$

#### Explanation:

First we need to find the slope of the line passing through the points: $\left(- 21 , 2\right) \mathmr{and} \left(- 32 , 5\right)$, the slope $m$ between the points:
$\left({x}_{1} , {y}_{1}\right) \mathmr{and} \left({x}_{2} , {y}_{2}\right)$ is given by:
$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$, so in this case:
$m = \frac{5 - 2}{- 32 - \left(- 21\right)}$, simplifying we get:
$m = \frac{3}{- 32 + 21} = \frac{3}{-} 11 = - \frac{3}{11}$
Now the perpendicular lines have slopes that are negative reciprocals, so if ${m}_{1} \mathmr{and} {m}_{2}$ are the slopes of the two perpendicular lines then:
${m}_{2} = - \frac{1}{m} _ 1$, therefore in this case:
${m}_{2} = - \frac{1}{- \frac{3}{11}} = \frac{11}{3}$