Question

What is the distance between `(5,-2,4)` and `(8,8,-1)`?

Answer 1

`d = sqrt(134)` or `~~ 11.58`

Explanation:

The formula for the distance for 3-dimensional coordinates is similar or 2-dimensional; it is: `d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2)`

We have the two coordinates, so we can plug in the values for `x`, `y`, and `z`:
`d = sqrt((-1-4)^2 + (8-(-2))^2 + (8-5)^2)`

Now we simplify:
`d = sqrt((-5)^2 + (10)^2 + (3)^2)`

`d = sqrt(25 + 100 + 9)`

`d = sqrt(134)`

If you want to leave it in exact form, you can leave the distance as `sqrt134`. However, if you want the decimal answer, here it is rounded to the nearest hundredth's place:
`d ~~ 11.58`

Hope this helps!