Question

What is the slope of any line perpendicular to the line passing through `(-9,8)` and `(3,-3)`?

Answer 1

12/11

Explanation:

The coordinates given can be used to determine the gradient.

In standard form the equation of a straight line is:

`" "y=mx+c`

Where `m` is the gradient (slope)

The trick is, that the gradient of the line perpendicular to the first is:

`" "-1/m`
So all you need to do is find the gradient of the first line then the other is just a matter of turning the first one 'upside down' and multiplying it by (-1)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let `(x_1,y_1) -> (-9,8)`
Let `(x_2,y_2)->(3,-3)`

Then the gradient is:

`m" "=" "(y_2-y_1)/(x_2-x_1)`

`=""(-3-8)/(3-(-9))`

`=""(-11)/(+12)`

`=-11/12`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So for the perpendicular line its gradient is:

`(-1)xx1/m" " ->" " (-1)xx(-12/11) =+12/11`