# What is the distance between (22,25,7) and (31,40,0)?

Apr 13, 2018

$\sqrt{355} \approx 18.8$

#### Explanation:

The distance between $\left({x}_{1} , {y}_{1} , {z}_{1}\right)$ and $\left({x}_{2} , {y}_{2} , {z}_{2}\right)$ is given by $\sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2} + {\left({z}_{2} - {z}_{1}\right)}^{2}}$

So for these two points we have:
$\sqrt{{\left(31 - 22\right)}^{2} + {\left(40 - 25\right)}^{2} + {\left(0 - 7\right)}^{2}} = \sqrt{{\left(9\right)}^{2} + {\left(15\right)}^{2} + {\left(- 7\right)}^{2}} = \sqrt{81 + 225 + 49} = \sqrt{355} \approx 18.8$