The segment joining A(-4, 2) and B(8, 10) is divided into four equal parts by three points.
Find the coordinates of the division point nearest to B.

The point nearest B divides AB in the ratio 3 : 1. $x=\frac{3\cdot 8+1\cdot (-4)}{4}=\frac{24-4}{4}=5$ and $y=\frac{3\cdot 10+1\cdot 2}{4}=\frac{32}{4}=8$, so the point is (5, 8). (-1, 4) uses the ratio 1 : 3 and therefore gives the point nearest A; (2, 6) is the middle one of the three points, i.e. the midpoint, not the one asked for; (4, 8) divides 24 - 4 by 5 instead of 4.