# What is the distance between (3,-1,-5) and (4,-3,6)?

Mar 4, 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((3-4)^2 + (-1-(-3))^2 + (-5-6)^2

$\sqrt{{\left(- 1\right)}^{2} + {2}^{2} + {\left(- 1 1\right)}^{2}}$

This becomes $\sqrt{1 + 4 + 121}$

Which is $\sqrt{126}$

This is equal to $3 \sqrt{14}$

This cannot be simplified further, so we are done.