A ropeway runs in a straight line from a base station B(-6, 2) to a hilltop H(9, 17).
A support tower stands at the point where $\frac{1}{3}$ of the ropeway, measured from B, has been covered.
Find the tower's coordinates.

One third of the way from B means BP : PH = 1 : 2. $x=\frac{1\cdot 9+2\cdot (-6)}{3}=\frac{9-12}{3}=-1$ and $y=\frac{1\cdot 17+2\cdot 2}{3}=\frac{21}{3}=7$, so the tower is at (-1, 7). (4, 12) measures the third from H instead of from B and so uses 2 : 1; (1.5, 9.5) is the midpoint, which is $\frac{1}{2}$ of the way, not $\frac{1}{3}$; (-1, 12) has the correct $x$ but then applies the 2 : 1 weighting to $y$.