# What is the length of the line segment between (5, -7) and (5, 11)?

Mar 4, 2017

The length of the line segment between the two points is $18$

#### 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:

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

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

$d = \sqrt{{0}^{2} + {18}^{2}}$

$d = \sqrt{{18}^{2}} = 18$