Question

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

Answer 1

`sqrt{601}`

Explanation:

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

`d^2 = (-4 - -4)^2 + (-2 - 3)^2 + (12 - -12)^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.