# How do you find in radical form, the distance between the two points (-3,7) and (4,2)?

Sep 25, 2016

$\sqrt{74}$

#### Explanation:

To calculate the distance use the $\textcolor{b l u e}{\text{distance formula}}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where $\left({x}_{1} , {y}_{1}\right) \text{ and " (x_2,y_2)" are 2 coordinate points}$

The 2 points here are (-3 ,7) and (4 ,2)

let $\left({x}_{1} , {y}_{1}\right) = \left(- 3 , 7\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(4 , 2\right)$

$\Rightarrow d = \sqrt{{\left(4 - \left(- 3\right)\right)}^{2} + {\left(2 - 7\right)}^{2}}$

$= \sqrt{49 + 25} = \sqrt{74} \leftarrow \text{ in radical form}$