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Math Help - Finding Point B Coordinates from Midpoint and Point A

  1. #1
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    Finding Point B Coordinates from Midpoint and Point A

    I have coordinate for point A and mid-point M. I want to find an unknown coordinate B from those two points. How to do that?

    I know I can do it manually cause it's a line segment but there must be a formula for making it simpler and quicker.
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by isharis View Post
    I have coordinate for point A and mid-point M. I want to find an unknown coordinate B from those two points. How to do that?

    I know I can do it manually cause it's a line segment but there must be a formula for making it simpler and quicker.
    M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)

    This is the midpoint formula. Note that you have

    \left(\frac{x_1+?}{2},\frac{y_1+?}{2}\right)

    So, all you have to do is insert the info where it must go like this

    Let's say that A=(1,3) and M=(2,4)

    Then to find the x value of the point B...

     <br />
\underbrace{\frac{1+?}{2}}_{\text{formula for midpoint}}=\overbrace{2}^{midpoint}<br />

    Do you see?
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  3. #3
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    Quote Originally Posted by isharis View Post
    I have coordinate for point A and mid-point M. I want to find an unknown coordinate B from those two points. How to do that?
    If c,d)" alt="Mc,d)" /> is the midpoint between p,q)~\&~Bx,y)" alt="Ap,q)~\&~Bx,y)" /> then x=2c-p~\&~y=2d-q.
    Last edited by Plato; September 12th 2009 at 07:23 AM.
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    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Plato View Post
    If c,d)..." alt="Mc,d)..." />
    I did lose some generality there, huh?

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    Thanks for the help, guys.
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    Quote Originally Posted by Plato View Post
    If c,d)" alt="Mc,d)" /> is the midpoint between p,q)~\&~Bx,y)" alt="Ap,q)~\&~Bx,y)" /> then x=2c-p~\&~y=2q-d.
    y should be ~y=2d-q
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  7. #7
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    Quote Originally Posted by isharis View Post
    y should be ~y=2d-q
    Yes. Thanks for the correction.
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