The point P divides the join of A(1, −2) and B(5, 4) externally in the ratio 3 : 1. What are the coordinates of P?

For external division the section formula uses a minus sign: $P=((m\cdot x$₂ − $n\cdot x$₁)/$(m-n),(m\cdot y$₂ − $n\cdot y$₁)/$(m-n)$). With $m:n=3:1,P$ = ((15 − 1)/2, (12 + 2)/2) = (7, 7). Using plus signs throughout gives the internal point (4, 2.5), the classic sign error.