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Exam-Style Questions on Voronoi Diagram

Problems on Voronoi Diagram adapted from questions set in previous Mathematics exams.

1.

IB Applications and Interpretation

Points A (-1 , -1) , B (-3 , 1) , C (1 , -3) , D (3 , 1) and E (-3 , -3) represent the locations of toilet buildings on a large caravan site. These points are illustrated on the following coordinate axes.
Horizontal scale: 2 units represents 1 km.
Vertical scale: 2 units represents 1 km.

Voronoi diagram

(a) Calculate the gradient of the line segment AD.

The Site Manager draws three straight lines to form an incomplete Voronoi diagram.

Voronoi diagram

(b) Find the equation of the line which would complete the Voronoi cell containing site A. Give your answer in the form \(ax + by + d = 0\) where \(a , b , d \in \mathbb Z \).

(c) In the context of the question, explain the significance of the Voronoi cell containing site A.


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