# What is the distance between (2,-14) and (-9,5)?

Dec 29, 2015

$\sqrt{482}$

#### 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 $\left(2 , - 14\right)$ and $\left({x}_{2} , {y}_{2}\right)$ represent $\left(- 9 , 5\right)$.
implies d=sqrt((-9-2)^2+(5-(-14))^2
implies d=sqrt((-11)^2+(5+14)^2
implies d=sqrt((-11)^2+(19)^2
$\implies d = \sqrt{121 + 361}$
$\implies d = \sqrt{482}$

Hence the distance between the given points is $\sqrt{482}$.