Question

Find an equation for the perpendicular bisector of the line segment whose endpoints are (-1,6) and (7,2).

Answer 1

`y=2x-2`

Explanation:

First, lets find the mid-point between those two points:

`((-1+7)/(2),(6+2)/(2))\\=(3,4)`

Now, lets find the gradient of the perpendicular bisector:

`-1*((6-2)/(-1-7))^(-1)\\=-1*(-8)/(4)\\=2`

Next, we can find the equation:

`y=2x+c\\4=2*3+c\\c=4-6\\c=-2\\\Rightarrow y=2x-2`