Question

What's the distance between points (3, 8, 0) and (−2, 9, −4), and the midpoint of the segment for which these are the endpoints?

Answer 1

`sqrt(42)` and `(1/2, 17/2, -2)`

Explanation:

In 3D, we can still use the pythagorean theorem:

`d^2 = (Delta x)^2 + (Delta y)^2 + (Delta z)^2`
`d^2 = (3 - (-2))^2 + (8 - 9)^2 + (0 - (-4))^2`
`d^2 = 5^2 + (-1)^2 + 4^2 = 42`
`d = sqrt(42)`

The halfway point can be found via
`bar x = (x_1+x_2)/2, bar y = (y_1+y_2)/2, barz = (z_1 + z_2)/2`
i.e.
`((3+ (-2))/2, (8 + 9)/2, (0 + (-4)) / 2) = (1/2, 17/2, -2)`