In what ratio does the $x$-axis divide the segment joining A(1, -5) and B(4, 7)?

On the $x$-axis $y=0$, so $\frac{7m+(-5)n}{m+n}=0$, giving $7m=5n$ and $\frac{m}{n}=\frac{5}{7}$. The ratio is 5 : 7. The answer 7 : 5 reads the ratio upside down, dividing $y_2$ by $y_1$ instead of the other way round; 5 : 12 quotes $m:(m+n)$, a part against the whole; 1 : 2 is a guess from the rough position of the crossing.