Long John Silver, a pirate, has buried his treasure on an island with five trees, located at the following points: $(30.0 \mathrm{m},-20.0 \mathrm{m}),(60.0 \mathrm{m}, 80.0 \mathrm{m}),(-10.0 \mathrm{m},-10.0 \mathrm{m})$
$(40.0 \mathrm{m},-30.0 \mathrm{m}),$ and $(-70.0 \mathrm{m}, 60.0 \mathrm{m}),$ all measured
relative to some origin, as in Figure $\mathrm{P} 3.62 .$ His ship's log instructs you to start at tree $A$ and move toward tree $B$, but to cover only one half the distance between $\mathrm{A}$ and $\mathrm{B}$. Then move toward tree $\mathrm{C}$, covering one third the distance between your currcnt location and $C$. Next move toward D covering one fourth the distance between where you are and D. Finally move towards $\mathrm{E}$, covering one fifth the distance between you and $\mathrm{E}$, stop, and dig. (a) Assume that you have correctly determined the order in which the pirate labeled the trees as $A, B, C, D,$ and $E,$ as shown in the figure. What are the coordinates of the point where his treasure is buried? (b) What if you do not really know the way the pirate labeled the trees? Rearrange the order of the trees [for instance, $\mathrm{B}(30 \mathrm{m},-20 \mathrm{m}), \mathrm{A}(60 \mathrm{m}, 80 \mathrm{m})$
$\mathrm{E}(-10 \mathrm{m},-10 \mathrm{m}), \quad \mathrm{C}(40 \mathrm{m},-30 \mathrm{m}), \quad$ and $\quad \mathrm{D}(-70 \mathrm{m}$
60 $\mathrm{m}$ ) ] and repeat the calculation to show that the answer does not depend on the order in which the trees are labeled.
(FIGURE CAN'T COPY)