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Exam-Style Question on Voronoi Diagram

A mathematics exam-style question with a worked solution that can be revealed gradually

List Of Questions Exam-Style Question More Voronoi Questions More on this Topic

Question id: 438. This question is similar to one that appeared on an IB AI Standard paper (specimen) for 2021. The use of a calculator is allowed.

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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If you need more practice try the self-checking interactive exercises called Voronoi Diagrams.

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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