Question

How do I find the equation of a perpendicular bisector of a line segment with the endpoints `(-2, -4)` and `(6, 4)`?

Answer 1

`x+y-2 = 0`

Explanation:

Let `(x,y)` be any point on the perpendicular bisector. From elementary geometry, we can easily see that this point must be equidistant from the two points `(-2,-4) and (6,4)`. Using the Euclidean distance formula gives us the equation

`(x+2)^2 + (y+4)^2 = (x-6)^2 + (y-4)^2`

This can be rewritten as

`(x+2)^2 - (x-6)^2 = (y-4)^2-(y+4)^2`

Using `a^2 -b^2 = (a+b)(a-b)`, this simplifies to

`8(2x-4) = -8*2y` which simplifies to

`x+y-2 = 0`