Apps. and Interpretation for IBDP Maths Ebook 1 | Page 131

2. The positions of two car parks A and B in a rectangular coordinate plane are at (4, 8)
and (8, 4) respectively. It is given that the boundary separating the Voronoi cells of A
and B passes through the origin.
(a) (i) Find the coordinates of the mid-point of AB .
(ii) Hence, write down the equation of the boundary separating the Voronoi
cells of A and B , giving the answer in slope-intercept form.
[3]
Another car park C(2, 4) is newly built, as shown in the following diagram:
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(b) (i) Write down the equation of the boundary separating the Voronoi cells of
B and C .
(ii)
(iii)
Find the coordinates of the intersection of the boundaries.
Hence, find the radius of the circle passing through all three car parks.
[4]
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