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Proving the equation of perpendicular bisector

  1. Mar 21, 2007 #1


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    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


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

    Help me with this proving things.


    2. Relevant equations

    3. The attempt at a solution

    Don't know where to start.

    I have no idea.
  2. jcsd
  3. Mar 21, 2007 #2


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    Staff Emeritus
    Science Advisor

    Try to find the equation of the line between the two points to start off with.
  4. Mar 21, 2007 #3


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    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.

  5. Mar 21, 2007 #4
    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: Mar 21, 2007
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