A straight canal runs from lock A(-3, -2) to lock B(9, 10).
Two sluice gates P and Q stand on it, with AP : PB = 1 : 3 and AQ : QB = 3 : 1.
Find the coordinates of gate Q.

For $Q$ the ratio is 3 : 1: $x=\frac{3\cdot 9+1\cdot (-3)}{4}=\frac{24}{4}=6$ and $y=\frac{3\cdot 10+1\cdot (-2)}{4}=\frac{28}{4}=7$, so $Q$ = (6, 7). (0, 1) is gate P (ratio 1 : 3), i.e. the wrong gate was read off; (3, 4) is the midpoint of AB, which lies between the two gates but is neither of them; (7, 6) writes the correct pair of numbers in the wrong order.