# What is the distance between (-45,-8) and (-37,2)?

Dec 29, 2015

$2 \sqrt{41}$

#### Explanation:

The distance formula for Cartesian coordinates is

d=sqrt((x_2-x_1)^2+(y_2-y_1)^2
Where ${x}_{1} , {y}_{1}$, and${x}_{2} , {y}_{2}$ are the Cartesian coordinates of two points respectively.
Let $\left({x}_{1} , {y}_{1}\right)$ represent $\left(- 45 , - 8\right)$ and $\left({x}_{2} , {y}_{2}\right)$ represent $\left(- 37 , 2\right)$.
implies d=sqrt((-37-(-45))^2+(2-(-8))^2
implies d=sqrt((-37+45)^2+(2+8)^2
implies d=sqrt((8)^2+(10)^2
$\implies d = \sqrt{64 + 100}$
$\implies d = 2 \sqrt{16 + 25}$

$\implies d = 2 \sqrt{41}$

Hence the distance between the given points is $2 \sqrt{41}$.