# What is the distance between (2, –3, 1)  and (0, 4, –2) ?

Mar 20, 2018

$\setminus \sqrt{62}$

#### Explanation:

Use this Distance Formula for 3D points (which is basically taken from the Pythagorean Theorem -- which I encourage you to see why).

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

Plug the points into the formula.
$\setminus \sqrt{{\left(2 - 0\right)}^{2} + {\left(- 3 - 4\right)}^{2} + \left(1 - \left(- 2\right)\right)}$
= $\setminus \sqrt{{2}^{2} + {\left(- 7\right)}^{2} + {\left(3\right)}^{2}}$
=$\setminus \sqrt{4 + 49 + 9}$
= $\setminus \sqrt{62}$