# How do you find the distance between (-2,4), (5,8)?

Dec 26, 2016

$\left\mid \left(- 2 , 4\right) : \left(5 , 8\right) \right\mid = \textcolor{g r e e n}{\sqrt{65}}$

#### Explanation:

The horizontal distance ($\Delta x$)between $\left(- 2 , 4\right)$ and $\left(5 , 8\right)$ is the absolute value of the difference between the $x$ components of the coordinates:
$\textcolor{w h i t e}{\text{XXX}} \Delta x = \left\mid 5 - \left(- 2\right) \right\mid = 7$

Similarly, the vertical distance ($\Delta y$)between $\left(- 2 , 4\right)$ and $\left(5 , 8\right)$ is the absolute value of the difference between the $y$ components of the coordinates:
$\textcolor{w h i t e}{\text{XXX}} \Delta x = \left\mid 8 - 4 \right\mid = 4$

Using the Pythagorean Theorem the distance between $\left(- 2 , 4\right)$ and $\left(5 , 8\right)$ is
$\textcolor{w h i t e}{\text{XXX}} d = \sqrt{{7}^{2} + {4}^{2}} = \sqrt{65}$