Apps. and Interpretation for IBDP Maths Ebook 1 | Page 133

4. The Voronoi diagram of three points A(1, 9), B(9, 9) and C(9,1) are formed.
(a) (i) Write down the equation of the boundary separating the Voronoi cells of
A and B .
(ii) Write down the equation of the boundary separating the Voronoi cells of
B and C .
[2]
A new point D(3, 3) is added to this Voronoi diagram, such that the coordinates of the
two points of intersection of the boundaries are (5, k ) and ( k , 5) , where k is a constant.
This is shown in the following diagram:
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(b) (i) Write down the coordinates of the mid-point of BD .
(ii) Hence, find the value of k .
(iii)
Find the decrease in the area of the Voronoi cell of B after D is added.
[6]
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