# What is the distance between (–5, –1, 1)  and (4, –1, 2)?

Jan 12, 2016

The distance formula for Cartesian coordinates is

d=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2
Where ${x}_{1} , {y}_{1} , {z}_{1}$, and ${x}_{2} , {y}_{2} , {z}_{2}$ are the Cartesian coordinates of two points respectively.
Let $\left({x}_{1} , {y}_{1} , {z}_{1}\right)$ represent $\left(- 5 , - 1 , 1\right)$ and $\left({x}_{2} , {y}_{2} , {z}_{2}\right)$ represent $\left(4 , - 1 , 2\right)$.
implies d=sqrt((4-(-5))^2+(-1-(-1))^2+(2-1)^2
implies d=sqrt((4+5)^2+(-1+1)^2+(2-1)^2
implies d=sqrt((9)^2+(0)^2+(1)^2
implies d=sqrt(81+0+1
implies d=sqrt(82
implies d=sqrt(82 units

Hence the distance between the given points is $\sqrt{82}$ units.