# How do you find the midpoint of (5√2, 2√3), and (√2, 2√3)?

Jun 14, 2017

See a solution process below:

#### Explanation:

The formula to find the mid-point of a line segment give the two end points is:

$M = \left(\frac{\textcolor{red}{{x}_{1}} + \textcolor{b l u e}{{x}_{2}}}{2} , \frac{\textcolor{red}{{y}_{1}} + \textcolor{b l u e}{{y}_{2}}}{2}\right)$

Where $M$ is the midpoint and the given points are:

$\left(\textcolor{red}{{x}_{1}} , \textcolor{red}{{y}_{1}}\right)$ and $\left(\textcolor{b l u e}{{x}_{2}} , \textcolor{b l u e}{{y}_{2}}\right)$

Substituting the values from the points in the problem gives:

$M = \left(\frac{\textcolor{red}{5 \sqrt{2}} + \textcolor{b l u e}{\sqrt{2}}}{2} , \frac{\textcolor{red}{2 \sqrt{3}} + \textcolor{b l u e}{2 \sqrt{3}}}{2}\right)$

$M = \left(\frac{\textcolor{red}{5 \sqrt{2}} + \textcolor{b l u e}{1 \sqrt{2}}}{2} , \frac{\textcolor{red}{2 \sqrt{3}} + \textcolor{b l u e}{2 \sqrt{3}}}{2}\right)$

M = ((5 + 1)sqrt(2))/2 , ((2 + 2)sqrt(3))/2)

$M = \left(\frac{6 \sqrt{2}}{2} , \frac{4 \sqrt{3}}{2}\right)$

$M = \left(3 \sqrt{2} , 2 \sqrt{3}\right)$