# How do you find the distance between (-3,17), (15,-7)?

May 13, 2017

$30 \text{ units}$

#### Explanation:

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

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

$\text{the points are } \left({x}_{1} , {y}_{1}\right) = \left(- 3 , 17\right) , \left({x}_{2} , {y}_{2}\right) = \left(15 , - 7\right)$

$d = \sqrt{{\left(15 - \left(- 3\right)\right)}^{2} + {\left(- 7 - 17\right)}^{2}}$

$\textcolor{w h i t e}{d} = \sqrt{{18}^{2} + {\left(- 24\right)}^{2}}$

$\textcolor{w h i t e}{d} = \sqrt{324 + 576}$

$\textcolor{w h i t e}{d} = \sqrt{900}$

$\textcolor{w h i t e}{d} = 30 \text{ units}$