Question

What is the distance between `(4, 4, 2)` and #(2, –3, 1) #?

Answer 1

The distance is `3sqrt6` or about `7.348` (rounded to nearest thousandth's place).

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

Now we simplify:
`d = sqrt((-2)^2 + (-7)^2 + (-1)^2)`

`d = sqrt(4 + 49 + 1)`

`d = sqrt(54)`

`d = 3sqrt6`

If you want to leave it in exact form, you can leave the distance as `3sqrt6`. However, if you want the decimal answer, here it is rounded to the nearest thousandth's place:
`d ~~ 7.348`

Hope this helps!