# What is the distance between (–2, 2, 6)  and (4, –1, 2)?

Jun 24, 2016

The distance between $\left(- 2 , 2 , 6\right)$ and $\left(4 , - 1 , 2\right)$ is $7.81$.

#### Explanation:

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

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

Hence distance between $\left(- 2 , 2 , 6\right)$ and $\left(4 , - 1 , 2\right)$ is

$\sqrt{{\left(4 - \left(- 2\right)\right)}^{2} + {\left(\left(- 1\right) - 2\right)}^{2} + {\left(2 - 6\right)}^{2}}$

= $\sqrt{{6}^{2} + {3}^{2} + {4}^{2}} = \sqrt{36 + 9 + 16} = \sqrt{61} = 7.81$.