# What is the slope of any line perpendicular to the line passing through (8,16) and (-7,12)?

Feb 13, 2016

Slope of line perpendicular to the line passing through $\left(8 , 16\right)$ and $\left(- 7 , 12\right)$ will be $- \frac{15}{4}$.

#### Explanation:

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 $\left(8 , 16\right)$ and $\left(- 7 , 12\right)$

the slope of line joining them is $\frac{12 - 16}{- 7 - 8}$ or $\frac{- 4}{-} 15$

i.e. $\frac{4}{15}$

Further product of slopes of two lines perpendicular to each other is $- 1$.

Hence slope of line perpendicular to the line passing through $\left(8 , 16\right)$ and $\left(- 7 , 12\right)$ will be $- \frac{1}{\frac{4}{15}}$ or $- \frac{15}{4}$.