Dividing a segment

You will write three functions: the distance between two points, the point that divides a segment in a ratio, and the ratio from a point on the segment. The checker uses both internal and external division.

The idea. The point that divides $AB$ in the ratio $m : n$ is $\dfrac{mB + nA}{m + n}$ in each coordinate. For an external division give a negative $n$, so that $m + n$ becomes $m - |n|$.

Your tasks.

1. Finish distance(p, q). Return the distance between two points of space.
2. Finish divide(p, q, m, n). Return the point as a tuple of three numbers.
3. Finish ratio_of(a, b, p). The point p lies on the line a to b. Return $\lambda = \dfrac{x - x_1}{x_2 - x}$ using the first coordinate in which b and p differ.