P(1, 4) divides the segment joining A(-5, 1) and B in the ratio 3 : 1.
Find the coordinates of B.

Let $B=(x,y)$. Then $\frac{3x+1\cdot (-5)}{4}=1$, so $3x=9$ and $x=3$; and $\frac{3y+1\cdot 1}{4}=4$, so $3y=15$ and $y=5$. Hence $B$ = (3, 5). (19, 13) solves the same two equations with the ratio written as 1 : 3, i.e. m and n swapped; (7, 7) treats $P$ as the midpoint of $AB$ and uses $B=2P-A$; (3, 4) copies P's $y$-value instead of solving for it.