# Finding Point B Coordinates from Midpoint and Point A

• Sep 12th 2009, 06:52 AM
isharis
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.
• Sep 12th 2009, 07:06 AM
VonNemo19
Quote:

Originally Posted by isharis
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 $B$...

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

Do you see?
• Sep 12th 2009, 07:13 AM
Plato
Quote:

Originally Posted by isharis
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 $M:(c,d)$ is the midpoint between $A:(p,q)~\&~B:(x,y)$ then $x=2c-p~\&~y=2d-q$.
• Sep 12th 2009, 07:15 AM
VonNemo19
Quote:

Originally Posted by Plato
If $M:(c,d)...$

I did lose some generality there, huh?(Doh)

(Hi)
• Sep 12th 2009, 07:16 AM
isharis
Thanks for the help, guys. :)
• Sep 12th 2009, 07:20 AM
isharis
Quote:

Originally Posted by Plato
If $M:(c,d)$ is the midpoint between $A:(p,q)~\&~B:(x,y)$ then $x=2c-p~\&~y=2q-d$.

y should be $~y=2d-q$
• Sep 12th 2009, 07:23 AM
Plato
Quote:

Originally Posted by isharis
y should be $~y=2d-q$

Yes. Thanks for the correction.