Answer: AP : PB = 1 : 3 (the dividing point is P(0, 27/4))
A point on the Y-axis has x = 0. Let P(0, y) divide AB in the ratio \(m:n\).
\[0=\frac{m(-9)+n(3)}{m+n}\ \Rightarrow\ 9m=3n\ \Rightarrow\ \frac mn=\frac13\]
Check: A is 3 units right of the Y-axis and B is 9 units left of it, so AP : PB = 3 : 9 = 1 : 3.
\[y=\frac{1(3)+3(8)}{4}=\frac{27}{4}\]
Note: the textbook answer key prints 3 : 1, which is the ratio PB : AP; measured from A, the ratio is 1 : 3.