4 . The diagram below shows the Voronoi diagram of three restaurants for takeaway meals , A , B and C , in a town bounded by the coordinate axes , the lines x � 8 and y � 8 , where 1 unit represents 1 km .
y
8
C ( 7 , 5 )
L
O |
A ( 3,1 ) B ( 5,1 ) |
8 |
x |
The straight line L is the boundary separating the Voronoi cells of B and C . It is given that ( 4 , 4 ) is a point on L .
( a ) ( i ) Find the gradient of L .
( ii ) Hence , find the equation of L , giving the answer in slopeintercept form .
Kimberly would like to find a restaurant closest to her office to minimize the delivery time of her meal during lunchtime . The position of her office is at ( 7 , 2.5 ) .
[ 4 ]
( b ) State the reason that she is indifferent from choosing the restaurant B and the restaurant C .
[ 1 ]
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