Thread: Finding Point B Coordinates from Midpoint and Point A

1. 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.

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

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?

3. 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 $\displaystyle Mc,d)$ is the midpoint between $\displaystyle Ap,q)~\&~Bx,y)$ then $\displaystyle x=2c-p~\&~y=2d-q$.

4. Originally Posted by Plato
If $\displaystyle Mc,d)...$
I did lose some generality there, huh?

5. Thanks for the help, guys.

6. Originally Posted by Plato
If $\displaystyle Mc,d)$ is the midpoint between $\displaystyle Ap,q)~\&~Bx,y)$ then $\displaystyle x=2c-p~\&~y=2q-d$.
y should be $\displaystyle ~y=2d-q$

7. Originally Posted by isharis
y should be $\displaystyle ~y=2d-q$
Yes. Thanks for the correction.