Voronoi Diagrams

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A real-world application of perpendicular bisectors is the construction of Voronoi Diagrams

The diagram below shows points in Singapore. The red dashed lines (formed from Perpendicular bisectors) demarcate the regions in Singapore nearest to each point. This is helpful to indicate the regions that each node might service in Singapore (Eg. Fire-Station). 

Drag the blue points around to see how the diagram changes.