# What is the distance between (–2, 0, 1)  and (0, 4, –2) ?

Mar 5, 2018

$d = 2 \sqrt{14}$

#### Explanation:

The distance between two points $\left({x}_{1} , {y}_{1} , {z}_{1}\right)$ and $\left({x}_{2} , {y}_{2} , {z}_{2}\right)$ in 3-space is given by the following formula

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

In the case of $\left(- 2 , 0 , 4\right)$ and $\left(0 , 4 , - 2\right)$, the distance between them is

$d = \sqrt{{\left(0 - - 2\right)}^{2} + {\left(4 - 0\right)}^{2} + {\left(- 2 - 4\right)}^{2}} = \sqrt{4 + 16 + 36} = \sqrt{56} = 2 \sqrt{14}$