Question

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

Answer 1

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 `(x_1,y_1,z_1)` represent `(-5,-1,1)` and `(x_2,y_2,z_2)` represent `(4,-1,2)`.
`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.