Find the coordinates of the point which divides the join of A(-3, 1) and B(7, 6) internally in the ratio 3 : 2.

With $m:n=3:2,x=\frac{3\cdot 7+2\cdot (-3)}{5}=\frac{21-6}{5}=3$ and $y=\frac{3\cdot 6+2\cdot 1}{5}=\frac{18+2}{5}=4$, so $P$ = (3, 4). (1, 3) comes from swapping $m$ and $n$, i.e. using $m{x}_1+n{x}_2$; (2, 3.5) is the midpoint, taken by ignoring the ratio; (3, 5) divides by 4 instead of $m+n=5$.