# How do you find the distance between the points (0,2) and (3,0) on a graph and what is the midpoint of the segment that joins them?

Aug 14, 2017

$\sqrt{13} , \left(\frac{3}{2} , 1\right)$

#### Explanation:

$\text{use the "color(blue)"distance formula}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\left({x}_{1} , {y}_{1}\right) = \left(0 , 2\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(3 , 0\right)$

$d = \sqrt{{\left(3 - 0\right)}^{2} + {\left(0 - 2\right)}^{2}} = \sqrt{9 + 4} = \sqrt{13}$

$\text{the midpoint of the segment is the average of the x}$
$\text{and y coordinates of the endpoints}$

$\text{midpoint } = \left[\frac{1}{2} \left(0 + 3\right) , \frac{1}{2} \left(2 + 0\right)\right] = \left(\frac{3}{2} , 1\right)$