# What is the distance between (2, -1) and (1, -5) on the coordinate plane?

Jan 13, 2017

$d = \sqrt{17}$ or $d = 4.1$ rounded to the nearest 10th

#### 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 two points from the problem and calculating gives the distance as:

$d = \sqrt{{\left(\textcolor{red}{1} - \textcolor{b l u e}{2}\right)}^{2} + {\left(\textcolor{red}{- 5} - \textcolor{b l u e}{- 1}\right)}^{2}}$

$d = \sqrt{{\left(- 1\right)}^{2} + {\left(- 4\right)}^{2}}$

$d = \sqrt{1 + 16}$

$d = \sqrt{17}$

$d = 4.1$ rounded to the nearest 10th