( a ) ( 1 ) Write down the gradient of QR .
( 2 ) Hence , write down the gradient of the perpendicular bisector of QR .
( 3 ) Find the equation of the perpendicular bisector of QR .
( 4 ) Find the coordinates of C .
( 5 ) Hence , find the length of the highway connecting B and C .
[ 9 ]
It is given that the length of the highway connecting A and D is 527 m , correct to the nearest metre .
( b ) ( 1 ) Write down the length of the highway connecting B and A .
( 2 ) Using the results from ( a )( 5 ) and ( b )( 1 ), find the total length of the highway in the town .
[ 4 ] In order to reduce the travelling time of the public transport , the urban planner is going to introduce the use of roundabouts to replace the use of traffic lights . The roundabouts are at all junctions A , B , C , D , G and H where more than one highway intersect , and the four vertices E , F , I and J , as shown in the following graph :
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