# How do you find the midpoint of the line segment joining (5,8) and (1,2)?

Dec 28, 2016

$\left(3 , 5\right)$

#### Explanation:

We can use the $\textcolor{b l u e}{\text{mid-point formula}}$

Given the coordinates of 2 points $A \left({x}_{1} , {y}_{1}\right) , B \left({x}_{2} , {y}_{2}\right)$ then the mid-point is found using.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{{M}_{A B} = \left[\frac{1}{2} \left({x}_{1} + {x}_{2}\right) , \frac{1}{2} \left({y}_{1} + {y}_{2}\right)\right]} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

The 2 points here are (5 ,8) and (1 ,2)

$\text{mid-point } = \left[\frac{1}{2} \left(5 + 1\right) , \frac{1}{2} \left(8 + 2\right)\right] = \left(3 , 5\right)$