Question

What is the distance between `(-2,1,-7)` and `(11,-5,4)`?

Answer 1

`sqrt326` or about `18.06` (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((11-(-2))^2 + (-5-1)^2 + (4-(-7))^2)`

Now we simplify:
`d = sqrt((13)^2 + (-6)^2 + (11)^2)`

`d = sqrt(169 + 36 + 121)`

`d = sqrt(326)`

If you want to leave it in exact form, you can leave the distance as `sqrt326`. However, if you want the decimal answer, here it is rounded to the nearest hundredth's place:
`d ~~ 18.06`

Hope this helps!