# What is the distance of (-5,2) and (-2,-6)?

Dec 24, 2016

$d = \sqrt{73}$

or

$d = 8.544$ rounded to the nearest thousandth

#### Explanation:

The formula for calculating the distance between two points is:

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

Substituting the two points we are given in this problem gives us:

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

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

$d = \sqrt{{\left(3\right)}^{2} + {\left(- 8\right)}^{2}}$

$d = \sqrt{9 + 64}$

$d = \sqrt{73}$

$d = 8.544$