The section formula and collinear points

You will write functions that divide a segment in a given ratio, find a midpoint, and test whether three points lie on one straight line. The checker uses the points of the lesson and of the problems.

The idea. If $AP : PB = m : n$, then $P = \dfrac{nA + mB}{m + n}$ for each coordinate. A negative $n$ gives an external division. Three points are collinear when $\overrightarrow{AB}$ and $\overrightarrow{AC}$ have proportional components.

Your tasks.

1. Finish divide(A, B, m, n). Return the point as a tuple of three numbers.
2. Finish midpoint(A, B). Use divide with $m = n = 1$.
3. Finish collinear(A, B, C). Return True when $\overrightarrow{AB}$ and $\overrightarrow{AC}$ are parallel. Compare every pair of components by cross-multiplying, so that a zero component does not cause trouble.