# What is the distance between (–10, –2, 2)  and (4, –1, 2)?

Jan 9, 2017

Distance between $\left(10 , - 2 , 2\right)$ and $\left(4 , - 1 , 2\right)$ is $6.083$.

#### Explanation:

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

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

Hence distance between $\left(10 , - 2 , 2\right)$ and $\left(4 , - 1 , 2\right)$ is

$\sqrt{{\left(4 - 10\right)}^{2} + {\left(- 1 - \left(- 2\right)\right)}^{2} + {\left(2 - 2\right)}^{2}}$

= $\sqrt{{\left(- 6\right)}^{2} + {\left(- 1 + 2\right)}^{2} + {0}^{2}}$

= $\sqrt{36 + 1 + 0}$

= $\sqrt{37}$

= $6.083$