Question

What is the slope of any line perpendicular to the line passing through `(10,2)` and `(7,-2)`?

Answer 1

`-3/4`

Explanation:

Let `m` be the slope of line passing through the given points and `m'` be the slope of line perpendicular to the line passing through the given points.

Since lines are perpendicular, therefore, the product of slopes will be equal to `-1`. i.e, `m*m'=-1`

`implies m'=-1/m`

`implies m'=-1/((y_2-y_1)/(x_2-x_1))`

`implies m'=-(x_2-x_1)/(y_2-y_1)`

Let `(7,-2)=(x_1,y_1)` and `(10,2)=(x_2,y_2)`

`implies m'=-(10-7)/(2-(-2))=-3/(2+2)=-3/4`

`implies m'=-3/4`

Hence, the slope of required line is `-3/4`.