# What is the distance between (0, 0, 8)  and (0, 6, 0) ?

##### 1 Answer
May 6, 2016

I assume that you know the distance formula (square root of sum of corresponding coordinates squared)
Well, that formula can actually be EXTENDED to the third dimension. (This is a very powerful thing in future mathematics)
What that means is that instead of the known

sqrt((a-b)^2 + (c-d)^2

We can extend this to be
sqrt((a-b)^2 + (c-d)^2 + (e-f)^2

This problem is beginning to look a lot easier huh?
We can just plug in the corresponding values into the formula

sqrt((0-0)^2 + (0-6)^2 + (8-0)^2

$\sqrt{{\left(0\right)}^{2} + {\left(- 6\right)}^{2} + {\left(8\right)}^{2}}$

This becomes $\sqrt{36 + 64}$

Which is $\sqrt{100}$

This would simplify to $10$

ALTERNATIVELY,
We can see that the x value doesn't change (goes from 0 to 0), so we can really just turn this into a 2 dimensional distance formula, meaning we don't have to extend this and just use

sqrt((a-b)^2 + (c-d)^2