Question

What is the distance between `(-3,5,-1)` and `(1,2,4)`?

Answer 1

The distance is `5sqrt2` or about `7.071` (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((1 - (-3))^2 + (2 - 5)^2 + (4 - (-1))^2)`

Now we simplify:
`d = sqrt((4)^2 + (-3)^2 + (5)^2)`

`d = sqrt(16 + 9 + 25)`

`d = sqrt(50)`

`d = 5sqrt2`

If you want to leave it in exact form, you can leave the distance as `5sqrt2`. However, if you want the decimal answer, here it is rounded to the nearest thousandth's place:
`d ~~ 7.071`

Hope this helps!