Proving the equation of perpendicular bisector

[ArL]

Homework Statement

My question is to :

Prove that the perpendicular bisector of the two points (x1, y1) and (x2, y2), in general form, is given by


Ax + By = C

where

A= 2(x2-x1), B= 2(y2 -y1) and C= y2^2 - y1^2 + x2^2 - x1^2

Help me with this proving things.

Thanks

Homework Equations

The Attempt at a Solution

Don't know where to start.

I have no idea.

 

[cristo]

Try to find the equation of the line between the two points to start off with.

 

[ArL]

I've done it.

However, I got some questions. (to check if I am right)

if it is (X2-X1)((X2+X1)*1/2)

is this transformed to

((X2-X1)(X2+X1))/2 ?

which is expended to (X2^2-X1^2)/2 ?

I am not good at those if there are fractions in it.

Please check my work.

Thanks.

 

[Werg22]

You can do it pretty quickly using parametric equations. You would have

$$D = 1/2 [x_{1} + x_{2}, y_{1} + y_{2}] + t[-{\Delta y},{\Delta x}]$$

And then you could easily find it.