Question

What is the distance between `(-5,13,4)` and `(2,-16,-2)`?

Answer 1

`d ~~ 30.4302`

Explanation:

We know that the distance formula for cartesian coordinates is as follows:

`sqrt((x_2-x_1)^2 + (y_2 - y_1)^2)`

In the case where there are three dimensions `(x, y, z)`, you just need to add another term to account for the z-coordinates.

`sqrt((x_2-x_1)^2 + (y_2 - y_1)^2 + (z_2 -z_1)^2)`

Plugging in the values from the given...

[Given]
`P_1: (-5, 13, 4)`
`P_2: (2, -16, -2)`

[Solution]
`d = sqrt((2-(-5))^2 + (-16-13)^2 + (-2-4)^2)`
`d = sqrt(7^2 + (-29)^2 + (-6)^2)`
`d = sqrt(49 + 841 + 36)`
`d = sqrt (926)`
`d ~~ 30.4302`