Apps. and Interpretation for IBDP Maths Ebook 1 | Page 138

Your Practice Set – Applications and Interpretation for IBDP Mathematics
3. The diagram below shows the Voronoi diagram of four farms, A , B , C and D , in a
rural town, where 1 unit represents 1 km. The points P(4, 5) and
intersections of the boundaries of Voronoi cells.
� 17 �
Q�5,
� are the
� 3 �
The government is planning to install a wireless network hotspot to provide internet
services in the town. However, farmers in the town hope that the location of the hotspot
should be farthest from all farms.
Two circles are constructed such that the centres are P and Q respectively, and passes
through the farms in adjacent Voronoi cells.
(a) (i) Find the radius of the circle centred at P .
(ii) Find the radius of the circle centred at Q .
(iii) Hence, determine which location is farthest from all four farms.
[5]
It is given that an electronic device cannot access to the wireless network if the horizontal
distance between the device and the hotspot is longer than 3.65 km.
128
(b)
State which farm will not be able to access to the wireless network if the hotspot
is installed at P .
[1]
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