Proving the equation of perpendicular bisector

  • Thread starter ArL
  • Start date
  • #1
ArL
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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.
 

Answers and Replies

  • #2
cristo
Staff Emeritus
Science Advisor
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Try to find the equation of the line between the two points to start off with.
 
  • #3
ArL
3
0
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
1,425
1
You can do it pretty quickly using parametric equations. You would have

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

And then you could easily find it.
 
Last edited:

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