Apps. and Interpretation for IBDP Maths Ebook 1 | Page 132

Your Practice Set – Applications and Interpretation for IBDP Mathematics
3. The positions of two supermarkets A and B in a rectangular coordinate plane are at
(2, 2) and (8, 8) respectively. It is given that the boundary separating the Voronoi cells
of A and B has the equation x �y � k , where k is a constant.
(a) (i) Find the coordinates of the mid-point of AB .
(ii) Hence, find the value of k .
Another supermarket C(6, 4) is newly opened, as shown in the following diagram:
[4]
The equation of the boundary separating the Voronoi cells of B and C is
y� �0.5x� 9.5 .
(b)
Find the coordinates of the intersection of the boundaries.
(c) State the significance of the Voronoi cell of B .
[3]
[1]
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