# What is the distance between (-12,4) and (8,3)?

Dec 29, 2015

$\sqrt{401}$

#### 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 $\left(- 12 , 4\right)$ and $\left({x}_{2} , {y}_{2}\right)$ represent $\left(8 , 3\right)$.
implies d=sqrt((8-(-12))^2+(3-4)^2
implies d=sqrt((8+12)^2+(-1)^2
implies d=sqrt((20)^2+(-1)^2
$\implies d = \sqrt{400 + 1}$
$\implies d = \sqrt{401}$

$\implies d = \sqrt{401}$

Hence the distance between the given points is $\sqrt{401}$.