Voronoi Diagrams:an Introduction Through Applications

Activity 1: "Where's the Closest Beef?"

Suppose the two points on the "map" below represent the sites of the only two MacDonnelly's fast-food restaurants in the entire state (the box.) Construct an accurate boundary between them such that anyone living in the state can tell which MacDonnelly's is closer to them. The map will then define the "service region" for each of the two restaurants.

Writing assignment: Explain how you constructed this boundary and describe what geometric properties this boundary has.