# What is the distance between (–5, 13)  and  (4, 7) ?

Apr 10, 2016

Distance between $\left(- 5 , 13\right)$ and $\left(4 , 7\right)$ is $10.817$

#### Explanation:

The distance between two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ is given by

$\sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$.

Hence distance between $\left(- 5 , 13\right)$ and $\left(4 , 7\right)$ is

$\sqrt{{\left(4 - \left(- 5\right)\right)}^{2} + {\left(7 - 13\right)}^{2}}$ or

$\sqrt{{\left(4 + 5\right)}^{2} + {\left(- 6\right)}^{2}}$ or

$\sqrt{81 + 36} = \sqrt{117} = 10.817$