Question

What is the distance between `(-5,3,9)` and `(-1,-4,1)`?

Answer 1

The distance is `sqrt129` or about `11.358` (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-(-5))^2 + (-4-3)^2 + (1-9)^2)`

Now we simplify:
`d = sqrt((4)^2 + (-7)^2 + (-8)^2)`

`d = sqrt(16 + 49 + 64)`

`d = sqrt(129)`

If you want to leave it in exact form, you can leave the distance as `sqrt129`. However, if you want the decimal answer, here it is rounded to the nearest thousandth's place:
`d ~~ 11.358`

Hope this helps!