# Midpoint Formula

## Key Questions

The coordinate of Midpoint $: \left(\frac{{x}_{1} + {x}_{2}}{2} , \frac{{y}_{1} + {y}_{2}}{2}\right)$

#### Explanation:

Midpoint Formula :

$\text{If "A(x_1,y_1) and B(x_2,y_2) " are the two point on the line ,}$

$\text{then midpoint M of the line segment " bar(AB) " is :}$

$M \left(\frac{{x}_{1} + {x}_{2}}{2} , \frac{{y}_{1} + {y}_{2}}{2}\right)$

You find the midpoint in exactly the same way with integers and fractions.

#### Explanation:

You find the midpoint in exactly the same way with integers and fractions, no matter whether they are common fractions, improper fractions or decimal fractions.

Add the two $x$- values together and divide by $2$

Add the two $y$-values together and divide by $2$

This will give a point, $M \left(x , y\right)$

• If you know one endpoint $\left({x}_{1} , {y}_{1}\right)$ and the midpoint $\left(a , b\right)$, but you do not know the other endpoint $\left({x}_{2} , {y}_{2}\right)$, then by rewriting the midpoint formula:

$\left\{\begin{matrix}a = \frac{{x}_{1} + {x}_{2}}{2} R i g h t a r r o w 2 a = {x}_{1} + {x}_{2} R i g h t a r r o w {x}_{2} = 2 a - {x}_{1} \\ b = \frac{{y}_{1} + {y}_{2}}{2} R i g h t a r r o w 2 b = {y}_{1} + {y}_{2} R i g h t a r r o w {y}_{2} = 2 b - {y}_{1}\end{matrix}\right.$

So, the unknown endpoint can be found by

$\left({x}_{2} , {y}_{2}\right) = \left(2 a - {x}_{1} , 2 b - {y}_{1}\right)$

I hope that this was helpful.

• The midpoint $M$ of the points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ is found by

$M = \left(\frac{{x}_{1} + {x}_{2}}{2} , \frac{{y}_{1} + {y}_{2}}{2}\right)$.

As you can see above, the each coordinate of $M$ is the average of the corresponding coordinates of the endpoints.

I hope that this was helpful.