Question

What is the distance between `(-8,9,-1)` and `(4,1,2)`?

Answer 1

`sqrt(217)`

Explanation:

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 `(-8,9,-1)` and `(x_2,y_2,z_2)` represent `(4,1,2)`.
`implies d=sqrt((4-(-8))^2+(1-9)^2+(2-(-1))^2`
`implies d=sqrt((12)^2+(-8)^2+(3)^2`
`implies d=sqrt(144+64+9)`
`implies d=sqrt217`

Hence the distance between the given points is `sqrt(217)`.