IB Maths AI SL AI 3.2 Voronoi diagrams questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

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Question 1

Paper 2Medium6 marks

Three weather stations record annual rainfall. Their coordinates are measured in kilometres.

Station	Coordinates	Annual rainfall (mm)
A	$(1,1)$	540
B	$(7,3)$	680
C	$(3,7)$	610

The Voronoi diagram assigns each location to its nearest station.

(a)

Find the equation of the boundary between the cells for stations A and B, in the form $y=mx+c$

[2]

(b)

The boundary between the cells for stations A and C has equation $x+3y=14$ The boundaries between the cells for A and B, and A and C, meet at a Voronoi vertex. Using your answer to part (a), find the coordinates of this vertex.

[3]

(c)

Estimate the annual rainfall at $Q=(2,5)$ using nearest-neighbour interpolation.

[1]

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