# What is the slope of any line perpendicular to the line passing through (10,2) and (7,-2)?

Jan 23, 2016

$- \frac{3}{4}$

#### Explanation:

Let $m$ be the slope of line passing through the given points and $m '$ be the slope of line perpendicular to the line passing through the given points.

Since lines are perpendicular, therefore, the product of slopes will be equal to $- 1$. i.e, $m \cdot m ' = - 1$

$\implies m ' = - \frac{1}{m}$

$\implies m ' = - \frac{1}{\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}}$

$\implies m ' = - \frac{{x}_{2} - {x}_{1}}{{y}_{2} - {y}_{1}}$

Let $\left(7 , - 2\right) = \left({x}_{1} , {y}_{1}\right)$ and $\left(10 , 2\right) = \left({x}_{2} , {y}_{2}\right)$

$\implies m ' = - \frac{10 - 7}{2 - \left(- 2\right)} = - \frac{3}{2 + 2} = - \frac{3}{4}$

$\implies m ' = - \frac{3}{4}$

Hence, the slope of required line is $- \frac{3}{4}$.