How do you find the distance between (-2,-1) and (-5,-5)?

1 Answer
Mar 7, 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 points in the problem gives:

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

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

$d = \sqrt{{\left(- 3\right)}^{2} + {\left(- 4\right)}^{2}}$

$d = \sqrt{9 + 16}$

$d = \sqrt{25}$

$d = 5$

The distance between the two points is $5$