The diagram below shows a city with five airports, and a plane flying in circles in the sky above it. The airspace is broken into 5 regions, each representing all the locations where the plane is closer to the airport located in that region than any other airport. If the plane needed to divert for an emergency landing, the pilots would land it at the closest airport possible: a region being highlighted represents the fact that if the plane were in that location when it needed to make an emergency landing, it would divert to airport in the highlighted region.

The above graph is known as a Voronoi diagram. Voronoi diagrams can seem intimidating at first, but in reality, all we need to construct them is a good understanding of lines. We'll walk through the step-by-step construction of one such diagram to get an understanding of what they are and how they work.

To begin our exploration of Voronoi diagrams, we need to define the term perpendicular bisector.