# How do you find the length of a slope Q (5,3) R (2, -1)?

Aug 17, 2015

The length of the line segment between Q$\left(5 , 3\right)$ and R$\left(2 , - 1\right)$ is $5$

#### Explanation:

Using the Pythagorean Theorem:

The horizontal distance (i.e. the $x$ distance) between Q and R is
$\textcolor{w h i t e}{\text{XXXX}}$$5 - 2 = 3$
The vertical distance (i.e. the $y$ distance) between Q and R is
$\textcolor{w h i t e}{\text{XXXX}}$$3 - \left(- 1\right) = 4$

The distance between Q and R (as given by the Pythagorean Theorem) is
$\textcolor{w h i t e}{\text{XXXX}}$$\sqrt{{3}^{2} + {4}^{2}} = 5$