A gas pipeline runs straight from a junction J(-2, 7) to a plant P.
A valve at V(4, 3) divides JP in the ratio 2 : 3 measured from J.
Find the coordinates of P.

Let $P=(x,y)$. Then $\frac{2x+3\cdot (-2)}{5}=4$, so $2x=26$ and $x=13$; and $\frac{2y+3\cdot 7}{5}=3$, so $2y=-6$ and $y=-3$. Hence $P$ = (13, -3). (10, -1) treats V as the midpoint of JP; (7, 1) reads the given ratio as JV : JP, a part against the whole, rather than JV : VP; (16, -5) stretches JV by a factor of 3 instead of $\frac{5}{2}$.