Question

What is the distance between `(–6, 3, 1)` and #(5, 6, 4) #?

Answer 1

`d ~~ 11.79`

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((5-(-6))^2 + (6-3)^2 + (4-1)^2)`

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

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

`d = sqrt(139)`

If you want to leave it in exact form, you can leave the distance as `sqrt139`. However, if you want the decimal answer, here it is rounded to the nearest hundredth's place:
`d ~~ 11.79`

Hope this helps!