4 . The diagram below shows the Voronoi diagram of four landfills , A , B , C and
D , in a city bounded by the coordinate axes , the lines x � 20 and y � 20 , where 1 unit on the grid represents 2 km . The points P and Q are the intersections of the boundaries of Voronoi cells . y
20
A
D
Q
P
B
C
0 20
There are two apartments , one is located at P and the another one is located at Q . Jack is going to rent a flat in one of the apartments , and he hopes that the flat selected to be as far as possible from all other landfills .
Two circles are constructed such that the centres are P and Q respectively , and passes through the landfills in adjacent Voronoi cells .
( a ) ( i ) Find the radius of the circle centred at P .
( ii ) Write down the radius of the circle centred at Q . x
( iii ) Hence , determine which apartment is farthest from all four landfills .
[ 4 ] ( b ) Write down the equation of the boundary separating the Voronoi cells of B and C , giving the answer in the form Ax � By �C � 0 .
© SE Production Limited 8 All Rights Reserved 2021
[ 2 ]