# What is the distance between the two endpoints in the graph: (2,3) (-3,-2)?

Dec 1, 2016

The distance between the two points is $5 \sqrt{2}$

#### Explanation:

First remember the distance formula:

$d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$

Note that you have been given the points (2,3) and (-3,-2).

Let ${x}_{1} = 2$, ${y}_{1} = 3$, ${x}_{2} = - 3$, and ${y}_{2} = - 2$

Now let's substitute these values into our distance formula.

$d = \sqrt{{\left(- 3 - 2\right)}^{2} + {\left(- 2 - 3\right)}^{2}}$

$d = \sqrt{{\left(- 5\right)}^{2} + {\left(- 5\right)}^{2}}$

$d = \sqrt{25 + 25}$

$d = \sqrt{50}$

$d = 5 \sqrt{2}$