5 . The Voronoi diagram of two points P ( 3 , 7 ) and Q ( 3 , 3 ) are formed .
( a ) Write down the equation of the boundary separating the Voronoi cells of P and Q .
A new point R ( 7 , 4 ) is added to this Voronoi diagram , as shown in the following diagram . y
[ 1 ]
10
P
R
Q
0 10 x
The equation of L , the boundary separating the Voronoi cells of Q and R , is kx � 2y
� 47 � 0 , where k is a constant .
( b ) ( i ) Write down the coordinates of the mid-point of QR .
( ii ) Find the value of k .
( iii ) Hence , find the coordinates of the intersection of the boundaries .
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