## Island Treasure

A young man was going through the attic of his grandfather's house and found a paper describing the location of a buried treasure on an particular Island. The note said that on the island one would find a gallows, an oak tree, and a pine tree. To locate the treasure one would begin at the gallows, walk to the pine tree, turn right 90 degrees and walk the same number of paces away from the pine tree. A spike was to be driven at that point. Then return to the gallows, walk to the oak tree and turn left 90 degrees and walk the same number of paces away from the oak tree. Drive a second spike in the ground. The midpoint of a string drawn between the two spikes would locate the treasure.

The young man and his friends mounted an expedition to the island but found the oak tree and the pine tree but no gallows. It had eliminated years ago without a trace. They returned home with the map below and no treasure.

Show them where to look for the treasure.

Try assuming an arbitrary location for the gallows and use GSP to construct the location of the two spikes. Now move the location of the gallows. What happens? Why?