Question

What is the distance between `(43,2,11)` and `(7,-1,26)`?

Answer 1

The distance is `3sqrt170` or `~~ 39.12`.

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((26-11)^2 + (-1-2)^2 + (7-43)^2)`

Now we simplify:
`d = sqrt((15)^2 + (-3)^2 + (-36)^2)`

`d = sqrt(225 + 9 + 1296)`

`d = sqrt(1530)`

`d = sqrt(9*170)`

`d = sqrt9sqrt170`

`d = 3sqrt170`

If you want to leave it in exact form, you can leave the distance as `3sqrt170`. However, if you want the decimal answer, here it is rounded to the nearest hundredth's place:
`d ~~ 39.12`

Hope this helps!