Proving the equation of perpendicular bisector

1. Mar 21, 2007

ArL

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. The attempt at a solution

Don't know where to start.

I have no idea.

2. Mar 21, 2007

cristo

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

3. Mar 21, 2007

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.

4. Mar 21, 2007

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.

Last edited: Mar 21, 2007
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