# What is the distance between the origin and the point (-19, 6)?

Feb 4, 2017

The distance is $\sqrt{397}$ or 19.9 rounded to the nearest tenth.

#### Explanation:

The origin is point (0, 0).
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 point given in the problem and the origin gives:

$d = \sqrt{{\left(\textcolor{red}{0} - \textcolor{b l u e}{- 19}\right)}^{2} + {\left(\textcolor{red}{0} - \textcolor{b l u e}{6}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{0} + \textcolor{b l u e}{19}\right)}^{2} + {\left(\textcolor{red}{0} - \textcolor{b l u e}{6}\right)}^{2}}$

$d = \sqrt{{19}^{2} + {\left(- 6\right)}^{2}}$

$d = \sqrt{361 + 36}$

$d = \sqrt{397} = 19.9$ rounded to the nearest tenth.