In what ratio does the point P(0, 6) divide the segment joining A(-2, 8) and B(4, 2)?

Let AP : PB = $m:n$. Using $x:0=\frac{4m-2n}{m+n}$, so $4m=2n$ and $\frac{m}{n}=\frac{1}{2}$. Check with $y:\frac{1\cdot 2+2\cdot 8}{3}=6$, which matches. Ratio = 1 : 2. The answer 2 : 1 measures the parts starting from B instead of A; 1 : 3 quotes AP : AB rather than AP : PB; 3 : 1 reverses that same error.