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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- Sep 12th 2009, 06:52 AMisharisFinding 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. - Sep 12th 2009, 07:06 AMVonNemo19
$\displaystyle M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

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? - Sep 12th 2009, 07:13 AMPlato
- Sep 12th 2009, 07:15 AMVonNemo19
- Sep 12th 2009, 07:16 AMisharis
Thanks for the help, guys. :)

- Sep 12th 2009, 07:20 AMisharis
- Sep 12th 2009, 07:23 AMPlato