# What is the distance between (–6, 3, 4)  and (–10, –2, 2) ?

Feb 13, 2016

The distance is $3 \sqrt{5}$.

#### Explanation:

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

Hence distance between(–6,3,4) and (–10,–2,2) is

$\sqrt{{\left(- 10 - \left(- 6\right)\right)}^{2} + {\left(- 2 - 3\right)}^{2} + {\left(2 - 4\right)}^{2}}$ or

$\sqrt{{\left(- 4\right)}^{2} + {\left(- 5\right)}^{2} + {\left(- 2\right)}^{2}}$ or

$\sqrt{16 + 25 + 4}$ or $\sqrt{45}$ or $3 \sqrt{5}$