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

Jun 14, 2018

$d = 1$

#### Explanation:

The formula for the distance for 3-dimensional coordinates is similar or 2-dimensional; it is: $d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2} + {\left({z}_{2} - {z}_{1}\right)}^{2}}$

We have the two coordinates, so we can plug in the values for $x$, $y$, and $z$:
$d = \sqrt{{\left(- 1 - 0\right)}^{2} + {\left(4 - 4\right)}^{2} + {\left(- 2 - \left(- 2\right)\right)}^{2}}$

Now we simplify:
$d = \sqrt{{\left(- 1\right)}^{2} + {\left(0\right)}^{2} + {\left(- 2 + 2\right)}^{2}}$

$d = \sqrt{1 + 0}$

$d = \sqrt{1}$

$d = 1$

Hope this helps!