Question 1

Paper 2Medium6 marks

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

StationCoordinatesAnnual rainfall (mm)
A(1,1)(1,1)540
B(7,3)(7,3)680
C(3,7)(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+cy=mx+c

[2]
(b)

The boundary between the cells for stations A and C has equation x+3y=14x+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)Q=(2,5) using nearest-neighbour interpolation.

[1]

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