# What is the distance between (5, –6, 4)  and (4, –1, 2)?

Aug 3, 2016

The distance between $\left(5 , - 6 , 4\right)$ and $\left(4 , - 1 , 2\right)$ is $5.477$

#### Explanation:

The distance between two points whose coordinates are $\left({x}_{1} , {y}_{1} , {z}_{1}\right)$ 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, the distance between $\left(5 , - 6 , 4\right)$ and $\left(4 , - 1 , 2\right)$ is

$\sqrt{{\left(4 - 5\right)}^{2} + {\left(\left(- 1\right) - \left(- 6\right)\right)}^{2} + {\left(2 - 4\right)}^{2}}$

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

= $\sqrt{1 + {5}^{2} + 4}$

= $\sqrt{1 + 25 + 4} = \sqrt{30} = 5.477$