# What is the distance between the origin and the midpoint of (1, 2) and (-3, 6)?

Feb 25, 2017

$\sqrt{17}$ or $4.123$ rounded to the nearest thousandth.

#### Explanation:

First, we use this formula to find the midpoint of these two points:

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

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

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

Substituting the values from the points in the problem gives:

$M = \left(\frac{\textcolor{red}{1} + \textcolor{b l u e}{- 3}}{2} , \frac{\textcolor{red}{2} + \textcolor{b l u e}{6}}{2}\right) = \left(- \frac{2}{2} , \frac{8}{2}\right) = \left(- 1 , 4\right)$

Next, we can use the distance formula to find the distance between the origin, which is (0, 0) and (-1, 4). The formula for calculating the distance between two points is:

$d = \sqrt{{\left(\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}\right)}^{2} + {\left(\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}\right)}^{2}}$

Substituting the values from the points in the problem gives:

$d = \sqrt{{\left(\textcolor{red}{- 1} - \textcolor{b l u e}{0}\right)}^{2} + {\left(\textcolor{red}{4} - \textcolor{b l u e}{0}\right)}^{2}} = \sqrt{{\left(- 1\right)}^{2} + {4}^{2}} = \sqrt{1 + 16} =$

$\sqrt{17}$ or $4.123$ rounded to the nearest thousandth.