# What is the distance between (7,35,6) and (-3,5,1)?

May 25, 2016

$d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2} + {\left({z}_{2} - {z}_{1}\right)}^{2}} \cong 32.02$

#### Explanation:

The distance between two points is simply the square root of the sum of the squares of the differences between the coordinates, or, in equation form:

$d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2} + {\left({z}_{2} - {z}_{1}\right)}^{2}}$

where our two points are:

$\left({x}_{1} , {y}_{1} , {z}_{1}\right)$ and $\left({x}_{2} , {y}_{2} , {z}_{2}\right)$

It doesn't matter which point you choose for either. Substituting the points we were given into this equation we get:

$d = \sqrt{{\left(7 - \left(- 3\right)\right)}^{2} + {\left(35 - 5\right)}^{2} + {\left(6 - 1\right)}^{2}}$

$d = \sqrt{{10}^{2} + {30}^{2} + {5}^{2}}$

$d = \sqrt{100 + 900 + 25}$

$d = \sqrt{1025} \cong 32.02$