# What is the distance between (3,-2,-2) and (5,-4,-6)?

Apr 3, 2018

I tried this:

#### Explanation:

The distance between the two points can be found using a kind of extended Pythagoras formula:

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

so, using our coordinates given in the problem:

$d = \sqrt{{\left(5 - 3\right)}^{2} + {\left[- 4 - \left(- 2\right)\right]}^{2} + {\left[- 6 - \left(- 2\right)\right)}^{2}} = \sqrt{4 + 4 + 16} = \sqrt{24} = 4.89 \text{units}$