## Exam-Style Question on Voronoi Diagram## A mathematics exam-style question with a worked solution that can be revealed gradually |

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.

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

The Site Manager draws three straight lines to form an incomplete 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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