# What is the equation of the line that passes through (-2,1)  and is perpendicular to the line that passes through the following points: (5,2),(-12,5)?

Feb 29, 2016

$17 x - 3 y + 37 = 0$

#### Explanation:

The slope of the line joining points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{1} , {y}_{1}\right)$ is given by $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} ^$. Hence slope of line joining $\left(5 , 2\right)$ and (−12,5) is $\frac{5 - 2}{- 12 - 5} = - \frac{3}{17}$

Hence slope of the line perpendicular to line joining $\left(5 , 2\right)$ and (−12,5) will be $- \frac{1}{- \frac{3}{17}}$ or $\frac{17}{3}$, as product of slopes of lines perpendicular to each other is $- 1$.

Hence equation of line passing through $\left(- 2 , 1\right)$ and having slope $\frac{17}{3}$ will be (using point-slope form)

$\left(y - 1\right) = \frac{17}{3} \left(x - \left(- 2\right)\right)$ or 3(y-1)=17(x+2)) or

$17 x - 3 y + 37 = 0$