Divide a line in a ratio

The section formula finds the point that splits a segment in a given ratio. You will write it, find the points of trisection, and then run it backwards to find a ratio.

The idea. $P = \left(\dfrac{m x_2 + n x_1}{m + n}, \dfrac{m y_2 + n y_1}{m + n}\right)$. For a point already on the segment, the ratio is $\dfrac{x_P - x_1}{x_2 - x_P}$, as long as the segment is not vertical.

Your tasks.

1. In divide, return the point that divides a to b in the ratio m : n.
2. Fill thirds with the two points of trisection of $(-3, 1)$ to $(9, 7)$.
3. In ratio, return $\dfrac{m}{n}$ for a point p on the segment from a to b.