The point P(4, t) divides the segment joining A(-2, 5) and B(7, -4) in the ratio 2 : 1. Find t.

$t=\frac{2\cdot (-4)+1\cdot 5}{2+1}=\frac{-8+5}{3}=\frac{-3}{3}=-1$. The $x$-coordinate confirms the ratio: $\frac{2\cdot 7+1\cdot (-2)}{3}=4$. The value 2 swaps m and n; 0.5 is the midpoint's $y$-value, taken by ignoring the ratio; 1 is a sign slip that reads -8 + 5 as +3.