# How do you find the distance between (-6.8,0.7), (-2.1, -6.2)?

Feb 10, 2017

See the entire solution process below:

#### 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 problem and calculating gives:

$d = \sqrt{{\left(\textcolor{red}{- 2.1} - \textcolor{b l u e}{- 6.8}\right)}^{2} + {\left(\textcolor{red}{- 6.2} - \textcolor{b l u e}{0.7}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{- 2.1} + \textcolor{b l u e}{6.8}\right)}^{2} + {\left(\textcolor{red}{- 6.2} - \textcolor{b l u e}{0.7}\right)}^{2}}$

$d = \sqrt{{\left(4.7\right)}^{2} + {\left(- 6.9\right)}^{2}}$

$d = \sqrt{22.09 + 47.61}$

$d = \sqrt{69.7} = 8.349$ rounded to the nearest thousandth