Question

What is the distance between `(8,1,-4)` and `(-3,6,-2)`?

Answer 1

`d = 5sqrt6` or `~~ 12.25`

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((-2-(-4))^2 + (6-1)^2 + (-3-8)^2)`

Now we simplify:
`d = sqrt((2)^2 + (5)^2 + (-11)^2)`

`d = sqrt(4 + 25 + 121)`

`d = sqrt(150)`

`d = 5sqrt6`

If you want to leave it in exact form, you can leave the distance as `5sqrt6`. However, if you want the decimal answer, here it is rounded to the nearest hundredth's place:
`d ~~ 12.25`

Hope this helps!