# How do you determine the length of a line segment whose endpoints are (6,4) and (-9,-4)#?

Jan 5, 2017

Use the formula for distance between two points: $d = \sqrt{{\left(\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}\right)}^{2} + {\left(\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}\right)}^{2}}$

#### Explanation:

Use the formula for distance between two points:

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

Substituting the points given in the problem yields:

$d = \sqrt{{\left(\textcolor{red}{- 9} - \textcolor{b l u e}{6}\right)}^{2} + {\left(\textcolor{red}{- 4} - \textcolor{b l u e}{4}\right)}^{2}}$

$d = \sqrt{- {15}^{2} + - {8}^{2}}$

$d = \sqrt{225 + 64}$

$d = \sqrt{289}$

d = 17