# What is the slope of any line perpendicular to the line passing through (24,-2) and (18,19)?

Mar 7, 2016

$m = \frac{2}{7}$

#### Explanation:

The first step is to calculate the gradient (m) of the line joining the 2 points using the $\textcolor{b l u e}{\text{ gradient formula }}$

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

where $\left({x}_{1} , {y}_{1}\right) \text{ and " (x_2,y_2) " are the coords of 2 points }$

let $\left({x}_{1} , {y}_{1}\right) = \left(24 , - 2\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(18 , 19\right)$

substitute these values into formula for m.

$\Rightarrow m = \frac{19 + 2}{18 - 24} = \frac{21}{-} 6 = - \frac{7}{2}$

Now if 2 lines with gradients  m_1 " and m_2 are perpendicular

then their product ${m}_{1} . {m}_{2} = - 1$

let ${m}_{2} \text{ be gradient of perpendicular line }$

$\Rightarrow {m}_{2} = \frac{- 1}{m} _ 1 = - \frac{1}{- \frac{7}{2}} = \frac{2}{7}$