# What is the distance between (–3, –2) and (5, 2)?

Apr 2, 2016

$4 \sqrt{5}$

#### Explanation:

The distance, $r$, between two points with coordinates $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ is given by

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

It is an application of Pythagoras Theorem.

Therefore, the distance between $\left(- 3 , - 2\right)$ and $\left(5 , 2\right)$ is

$\sqrt{{\left(- 3 - 5\right)}^{2} + {\left(- 2 - 2\right)}^{2}} = \sqrt{64 + 16}$

$= \sqrt{80}$

$= 4 \sqrt{5}$

Apr 2, 2016

$4 \sqrt{5}$

#### Explanation:

color(blue)((-3,-2)and(5,2)

Use the distance formula

So,

color(purple)(x_1=-3,x_2=5

color(purple)(y_1=-2,y_2=2

$\therefore d = \sqrt{{\left(- 3 - 5\right)}^{2} + {\left(- 2 - 2\right)}^{2}}$

$\rightarrow \sqrt{{\left(- 8\right)}^{2} + {\left(- 4\right)}^{2}}$

$\rightarrow \sqrt{64 + 16}$

$\rightarrow \sqrt{80}$

$\rightarrow \sqrt{16 \cdot 5}$

color(green)(rArr4sqrt5