The point C(5, 1) lies on the segment joining A(-1, 4) and B(9, -1).
Use the section formula to find the ratio AC : CB.

Let AC : CB = $m:n$. From $x:5=\frac{9m-n}{m+n}$, so $5m+5n=9m-n$ and $6n=4m$, giving $\frac{m}{n}=\frac{3}{2}$. Check with $y:\frac{3\cdot (-1)+2\cdot 4}{5}=\frac{5}{5}=1$, which matches. The ratio is 3 : 2. The answer 2 : 3 reverses $m$ and $n$; 3 : 5 quotes AC : AB rather than AC : CB; 5 : 3 combines both mistakes.