# What is the slope of any line perpendicular to the line passing through (25,-2) and (30,34)?

Sep 3, 2016

Slope of line perpendicular to the one joining $\left(25 , - 2\right)$ and $\left(30 , 34\right)$ is $- \frac{5}{36}$.

#### Explanation:

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

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

Hence slope of line joining $\left(25 , - 2\right)$ and $\left(30 , 34\right)$ is

$\frac{34 - \left(- 2\right)}{30 - 25}$

= $\frac{36}{5}$

As the product of slopes of two lines perpendicular to each other is $- 1$, slope of line perpendicular to the one joining $\left(25 , - 2\right)$ and $\left(30 , 34\right)$ is

$- \frac{1}{\frac{36}{5}} = - \frac{5}{36}$