Question

How do I write an equation for the perpendicular bisector of the segment joining the points `(5,-4)` and `(-3,-2)`?

Answer 1

`y=4x-7`

Explanation:

The slope of the line in which the two points lay is `k=Delta_y/Delta_x`. The slope of the line perpendicular to that one is `p=-1/k=-Delta_x/Delta_y`.
`p=-(x_2-x_1)/(y_2-y_1)=-(5+3)/(-4+2)=8/2=4`

The midpoint is `(1,-3)`

So the require equation is
`(y+3)=4(x-1)`
`y=4x-4-3`
`y=4x-7`