Finding Point B Coordinates from Midpoint and Point A

isharis · #1 $Old$ September 12th, 2009, 07:52 AM

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.

VonNemo19 · #2 $Old$ September 12th, 2009, 08:06 AM

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 $B$ ...

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

Do you see?