The point P(−1, 3) divides the segment joining A(−5, 7) and B in the ratio 2 : 3. Find B.

Let $B=(x,y)$. Section formula with m : $n=2:3:\frac{2x+3(-5)}{5}=-1$ → $2x-15=-5$ → $x=5$, and $\frac{2y+3(7)}{5}=3$ → $2y+21=15$ → $y=-3$. So $B$ = (5, −3); checking, (−1, 3) does divide A(−5, 7) to (5, −3) in 2 : 3. Treating $P$ as the MIDPOINT of $AB$ gives $B=2P-A$ = (3, −1), but $P$ is not the midpoint here. Misreading the ratio as 2 : 1 gives (1, 1).