Today's cell phones have amazing location-based capabilities. They know where you are, map where you're going, tell you which route to take, and find a place to buy a coffee on the way. How do they DO that? How many cell towers does it take to pinpoint your location?

In this lesson, students describe the location information provided by a cell phone tower, explain why loci from at least three towers are required to pinpoint a customer's location, and consider the tradeoff between coverage and "locatability" when a cell phone company chooses a new tower location.

### Students will

• Describe all the points a given distance from a cell tower as a circle with center and radius, and draw the locus using a compass
• Analyze the intersections of loci obtained from two towers, and explain that given this information, there are two possible locations for the customers
• Understand that data from three cell towers is required to guarantee a customer's location can be pinpointed
• Given the maximum range of cell towers in a city, estimate both the total area covered, and the area of intersection in which customers' locations can be pinpointed
• Decide where to build a new cell tower, considering the tradeoff between coverage and locatability

### Before you begin

Students should be able to plot a point in Quadrant I, and use a compass to draw a circle given its center and radius.