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Thread: 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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    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.
    $\displaystyle M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

    This is the midpoint formula. Note that you have

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

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

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

    Then to find the x value of the point $\displaystyle B$...

    $\displaystyle
    \underbrace{\frac{1+?}{2}}_{\text{formula for midpoint}}=\overbrace{2}^{midpoint}
    $

    Do you see?
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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 $\displaystyle Mc,d)$ is the midpoint between $\displaystyle Ap,q)~\&~Bx,y)$ then $\displaystyle x=2c-p~\&~y=2d-q$.
    Last edited by Plato; Sep 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 $\displaystyle Mc,d)...$
    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 $\displaystyle Mc,d)$ is the midpoint between $\displaystyle Ap,q)~\&~Bx,y)$ then $\displaystyle x=2c-p~\&~y=2q-d$.
    y should be $\displaystyle ~y=2d-q$
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    Quote Originally Posted by isharis View Post
    y should be $\displaystyle ~y=2d-q$
    Yes. Thanks for the correction.
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