Question

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

Answer 1

The distance is `3sqrt10` or about `9.49` (rounded to nearest hundredth'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((-2-1)^2 + (-3-(-3))^2 + (4-(-5))^2)`

(I wasn't sure if the `3-` meant `3` or `-3`, so I assumed it was `-3`)

Now we simplify:
`d = sqrt((-3)^2 + (0)^2 + (9)^2)`

`d = sqrt(9+0+81)`

`d = sqrt(90)`

`d = 3sqrt10`

If you want to leave it in exact form, you can leave the distance as `3sqrt10`. However, if you want the decimal answer, here it is rounded to the nearest hundredth's place:
`d ~~ 9.49`

Hope this helps!