# What is the slope of any line perpendicular to the line passing through (12,-5) and (-1,7)?

Mar 29, 2017

Slope of the perpendicular to the line joining $\left(12 , - 5\right)$ and $\left(- 1 , 7\right)$ is $\frac{13}{12}$

#### Explanation:

Slope of a line joining $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ is

$\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

Therefore slope of line joining $\left(12 , - 5\right)$ and $\left(- 1 , 7\right)$ is

$\frac{7 - \left(- 5\right)}{- 1 - 12} = \frac{12}{- 13} = - \frac{12}{13}$

As product of slopes of two lines perpendicular to each other is $- 1$

slope of the perpendicular to the line joining $\left(12 , - 5\right)$ and $\left(- 1 , 7\right)$ is

$\frac{- 1}{- \frac{12}{13}} = \left(- 1\right) \times \left(- \frac{13}{12}\right) = \frac{13}{12}$