Water Reservoir Problems

1. You work for the World Health Organization (WHO) and have been asked to locate a new water reservoir that two villages will use. Optimally you want to locate the reservoir so that it is equidistant from the villages. Where should the reservoir be placed (theoretically)? What are some real-life situations where the equidistant location would not be desirable?
   
   
2. You have now been asked to locate a new reservoir that three villages will use. Each person should use Sketchpad to create three villages. Now create a fourth point that you expect would work for the reservoir - measure the distances from your reservoir and drag the reservoir around until you have (approximately) found the equidistant location.
   
   
   Next construct the triangle formed by the villages and the perpendicular bisectors of the sides, showing the circumcenter is at your equidistant location for the reservoir.
   
   Then change the location of your villages. You will have to move your reservoir to the circumcenter after you move a village. Will the reservoir always be located inside the triangle formed by the villages?
   
   
3. You are helping the WHO to locate another reservoir, but this time four villages (in 3-space!) will use the reservoir. Describe how you might locate the best spot for the reservoir by looking at different examples. Is there an equidistant spot in certain kinds of village configurations, but not in others? How about if there are more than four villages?
   
   
4. Where does the university drinking water come from?