The segment joining A(-6, 4) and B(3, -8) is cut by the $y$-axis at a point P.
Find the ratio AP : PB and the coordinates of P.

On the $y$-axis $x=0$, so $\frac{3m-6n}{m+n}=0$, giving $3m=6n$ and $m:n=2$ : 1. Then $y=\frac{2\cdot (-8)+1\cdot 4}{3}=\frac{-16+4}{3}=-4$, so P(0, -4). The options with 1 : 2 invert $m$ and $n$; P(0, -2) uses the plain average $\frac{4+(-8)}{2}$ of the $y$-values instead of the 2 : 1 weighted average.