Question

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

Answer 1

`color(blue)(11/48)`

Explanation:

If a line has a slope of `color(green)(m)`
then any line perpendicular to it has a slope of `color(green)(""(-1/m))`

A line through `(-9,5)` and `(2,-43)` has a slope of
`color(white)("XXX")m=(Deltay)/(Deltax)=(5-(-43))/(-9-2)=-48/11`

So any line perpendicular to this has a slope of
`color(white)("XXX")11/48`

Answer 2

Reqd. Slope `=11/48.`

Explanation:

Let us name the line passing thro. two given pts. `L`.

Then, Slope of `L = (5-(-43))/(-9-2)=48/-11.`

Therefore, the slope of any line perp. to `L` is given by `-1/(48/-11)=11/48`