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

Jan 23, 2016

The distance formula is of the form:
${d}^{2} = \left(\Delta {x}^{2}\right) + {\left(\Delta y\right)}^{2} + {\left(\Delta z\right)}^{2}$ where $\Delta$ stands for "change in"
Or the difference between one and the other.

#### Explanation:

Just we just fill in the $x , y , z$ co-ordinates:
${d}^{2} = {\left(- 2 - 5\right)}^{2} + {\left(2 - - 6\right)}^{2} + {\left(6 - 4\right)}^{2}$
${d}^{2} = {\left(- 7\right)}^{2} + {\left(8\right)}^{2} + {\left(2\right)}^{2} = 49 + 64 + 4 = 117$

And the distance $d$ is the square root of this:
$d = \sqrt{117} \approx 10.82$