# How do you find the distance of (2, -3) and (5, -4)?

Aug 22, 2017

See a 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 points in the problem gives:

$d = \sqrt{{\left(\textcolor{red}{5} - \textcolor{b l u e}{2}\right)}^{2} + {\left(\textcolor{red}{- 4} - \textcolor{b l u e}{- 3}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{5} - \textcolor{b l u e}{2}\right)}^{2} + {\left(\textcolor{red}{- 4} + \textcolor{b l u e}{3}\right)}^{2}}$

$d = \sqrt{{3}^{2} + {\left(- 1\right)}^{2}}$

$d = \sqrt{9 + 1}$

$d = \sqrt{10}$

Or

$d = 3.162$ rounded to the nearest thousandth.