How do you find the distance between the points (5,-1), (11,7)?

Jul 17, 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:

$d = \sqrt{{\left(\textcolor{red}{11} - \textcolor{b l u e}{5}\right)}^{2} + {\left(\textcolor{red}{7} - \textcolor{b l u e}{- 1}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{11} - \textcolor{b l u e}{5}\right)}^{2} + {\left(\textcolor{red}{7} + \textcolor{b l u e}{1}\right)}^{2}}$

$d = \sqrt{{6}^{2} + {8}^{2}}$

$d = \sqrt{36 + 64}$

$d = \sqrt{100}$

$d = 10$