# What is the slope of any line perpendicular to the line passing through (-9,5) and (2,-43)?

Jul 8, 2016

$\textcolor{b l u e}{\frac{11}{48}}$

#### Explanation:

If a line has a slope of $\textcolor{g r e e n}{m}$
then any line perpendicular to it has a slope of color(green)(""(-1/m))

A line through $\left(- 9 , 5\right)$ and $\left(2 , - 43\right)$ has a slope of
$\textcolor{w h i t e}{\text{XXX}} m = \frac{\Delta y}{\Delta x} = \frac{5 - \left(- 43\right)}{- 9 - 2} = - \frac{48}{11}$

So any line perpendicular to this has a slope of
$\textcolor{w h i t e}{\text{XXX}} \frac{11}{48}$

Jul 8, 2016

Reqd. Slope $= \frac{11}{48.}$
Let us name the line passing thro. two given pts. $L$.
Then, Slope of $L = \frac{5 - \left(- 43\right)}{- 9 - 2} = \frac{48}{-} 11.$
Therefore, the slope of any line perp. to $L$ is given by $- \frac{1}{\frac{48}{-} 11} = \frac{11}{48}$