# How do you find the distance between points (-11, 9), (3,-4)?

##### 1 Answer
Jan 28, 2017

sqrt365≈19.105" to 3 dec. places"

#### Explanation:

To calculate the distance between 2 points use the $\textcolor{b l u e}{\text{distance formula}}$

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

The 2 points here are (-11 ,9) and (3 ,-4)

let $\left({x}_{1} , {y}_{1}\right) = \left(- 11 , 9\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(3 , - 4\right)$

$d = \sqrt{{\left(3 - \left(- 11\right)\right)}^{2} + {\left(- 4 - 9\right)}^{2}}$

$= \sqrt{{14}^{2} + {\left(- 13\right)}^{2}} = \sqrt{196 + 169} = \sqrt{365}$

rArr"distance between points " =sqrt365≈19.105