# What is the distance between (-4,-2,12) and (-4,3,-12)?

Apr 25, 2018

$\sqrt{601}$

#### Explanation:

The Pythagorean Theorem gives the squared distance as the sum of squares of the difference of each coordinate:

${d}^{2} = {\left(- 4 - - 4\right)}^{2} + {\left(- 2 - 3\right)}^{2} + {\left(12 - - 12\right)}^{2}$

${d}^{2} = {0}^{2} + {5}^{2} + {24}^{2} = 601$

$d = \sqrt{601}$.

There's not really another way to check it other than to do it again. Oh yeah, we could have someone else do it. My go-to expert is Wolfram Alpha. Alpha's even kind enough to work out the approximation and draw a picture. It really is an amazing gift to the world.