The horizontal line $y=6$ cuts the segment joining A(3, -3) and B(-5, 9) at a point P.
Find the ratio AP : PB and the coordinates of P.

Let AP : PB = $m:n$. Then $\frac{9m-3n}{m+n}=6$, so $9m-3n=6m+6n,3m=9n$ and $m:n=3$ : 1. Then $x=\frac{3\cdot (-5)+1\cdot 3}{4}=\frac{-12}{4}=-3$, giving P(-3, 6). The 1 : 3 option inverts $m$ and $n$, and its point (1, 0) does not even lie on $y=6$; 1 : 1 assumes the midpoint, whose $y$ is 3; the last option has the correct ratio but copies the midpoint's $y$-value.