# Find the slope of any line perpendicular to the line passing through (24,−2) and (18,19)

Find the slope of any line perpendicular to the line passing through (24,−2) and (18,19)
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Besagnoe9
The first step is to calculate the gradient (m) of the line joining the 2 points using the gradient formula
$m=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$
where $\left({x}_{1},{y}_{1}\right)\phantom{\rule{1ex}{0ex}}\text{and}\phantom{\rule{1ex}{0ex}}\left({x}_{2},{y}_{2}\right)\phantom{\rule{1ex}{0ex}}\text{are the coords of 2 points}\phantom{\rule{1ex}{0ex}}$
let $\left({x}_{1},{y}_{1}\right)=\left(24,-2\right)\phantom{\rule{1ex}{0ex}}\text{and}\phantom{\rule{1ex}{0ex}}\left({x}_{2},{y}_{2}\right)=\left(18,19\right)$
substitute these values into formula for m.
$⇒m=\frac{19+2}{18-24}=\frac{21}{-6}=-\frac{7}{2}$
Now if 2 lines with gradients ${m}_{1}\text{}\phantom{\rule{1ex}{0ex}}\text{and}\phantom{\rule{1ex}{0ex}}{m}_{2}$ are perpendicular
then their product ${m}_{1}.{m}_{2}=-1$
let ${m}_{2}\phantom{\rule{1ex}{0ex}}\text{be gradient of perpendicular line}\phantom{\rule{1ex}{0ex}}$
$⇒{m}_{2}=\frac{-1}{{m}_{1}}=-\frac{1}{-\frac{7}{2}}=\frac{2}{7}$