How do you find the distance between the points (-8,-4), (-3,-8)?

Feb 20, 2017

The distance between the points is $\sqrt{41}$ or $6.403$ rounded to the nearest thousandth.

Explanation:

The formula for calculating the distance between two points is:

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

Substituting the values from the points in the problem gives:

$d = \sqrt{{\left(\textcolor{red}{- 3} - \textcolor{b l u e}{- 8}\right)}^{2} + {\left(\textcolor{red}{- 8} - \textcolor{b l u e}{- 4}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{- 3} + \textcolor{b l u e}{8}\right)}^{2} + {\left(\textcolor{red}{- 8} + \textcolor{b l u e}{4}\right)}^{2}}$

$d = \sqrt{{5}^{2} + {\left(- 4\right)}^{2}}$

$d = \sqrt{25 + 16}$

$d = \sqrt{41} = 6.403$ rounded to the nearest thousandth.