A cable car travels in a straight line from station A(2, 3) to station B(17, 13).
A camera is mounted at the point that is $\frac{2}{5}$ of the way along AB, measured from A.
Find the camera's coordinates.

Being $\frac{2}{5}$ of the way from A means AP : PB = 2 : 3. $x=\frac{2\cdot 17+3\cdot 2}{5}=\frac{40}{5}=8$ and $y=\frac{2\cdot 13+3\cdot 3}{5}=\frac{35}{5}=7$, so the camera is at (8, 7). (11, 9) reads $\frac{2}{5}$ as the share nearer B and so uses 3 : 2; (9.5, 8) is the midpoint, i.e. $\frac{1}{2}$ of the way; (8, 8) gets $x$ right but then takes the plain average of the $y$-values.