# Find the slope of any line perpendicular to the line passing through (3,−2) and (12,19)

Find the slope of any line perpendicular to the line passing through (3,−2) and (12,19)
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Giancarlo Phelps
If the two points are $\left({x}_{1},{y}_{1}\right)$ and $\left({x}_{2},{y}_{2}\right)$, the slope of the line joining them is defined as
$\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$ or $\frac{{y}_{1}-{y}_{2}}{{x}_{1}-{x}_{2}}$
As the points are (3,−2) and (12,19)
the slope of line joining them is $\frac{19-\left(-2\right)}{12-3}$ or $\frac{21}{9}$
i.e. $\frac{7}{3}$
Further product of slopes of two lines perpendicular to each other is −1.
Hence slope of line perpendicular to the line passing through (3,−2) and (12,19) will be $-\frac{1}{\frac{7}{3}}$ or $-\frac{3}{7}$