# What is the distance between (-2,-9,10) and (22,5,-6)?

$d = \sqrt{1028}$

$d = 32.06243908$

#### Explanation:

In Euclidean three-space, the distance between points $\left({x}_{1} , {y}_{1} , {z}_{1}\right)$ and $\left({x}_{2} , {y}_{2} , {z}_{2}\right)$ is

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

$d = \sqrt{{\left(22 - - 2\right)}^{2} + {\left(5 - - 9\right)}^{2} + {\left(- 6 - 10\right)}^{2}}$

$d = \sqrt{{\left(24\right)}^{2} + {\left(14\right)}^{2} + {\left(- 16\right)}^{2}}$

$d = \sqrt{576 + 196 + 256}$

$d = \sqrt{1028}$

$d = 32.06243908$

God bless....I hope the explanation is useful.