Question

What is the distance between `(-1,4,1)` and `(6,-7,-2)`?

Answer 1

`d = sqrt(179)` or `~~ 13.38`

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 + (-7-4)^2 + (6-(-1))^2)`

Now we simplify:
`d = sqrt((-3)^2 + (-11)^2 + (7)^2)`

`d = sqrt(9 + 121 + 49)`

`d = sqrt(179)`

If you want to leave it in exact form, you can leave the distance as `sqrt179`. However, if you want the decimal answer, here it is rounded to the nearest hundredth's place:
`d ~~ 13.38`

Hope this helps!