1 . Sardar owns a plot of land in the shape of a pentagon ABCDE , where the boundaries AE and BC are parallel . The dimension can be represented on a coordinate plane , where 1 unit on the plane represents 1m . The coordinates of A , B , C and E are A ( 10,10 ) , B ( 10,110 ) , C ( 50,110 ) and E ( 125,10 ) respectively . The equation of the boundary CD is 7x�24y�2990 � 0.
( a ) It is given that F ( 98 , f ) lies on CD . Find f .
( b ) Write down the gradient of CD .
The boundaries CD and DE are perpendicular to each other .
[ 2 ]
[ 1 ]
( c ) ( i ) Find the gradient of DE .
( ii ) Hence , show that the equation of DE is 24x�7y�2930 � 0 . [ 5 ]
( d ) Write down the coordinates of D , the point of intersection between the boundaries CD and DE .
[ 2 ]
( e ) Show that F is the mid-point of CD . [ 2 ]
( f ) Find the length of the boundary DE .
[ 2 ]
It is also given that the length of the boundary CD is 100 m .
( g ) Find the area of the triangle CDE .
( h ) Hence , find the total area of the plot of land .
[ 2 ]
[ 4 ]
© SE Production Limited 2 All Rights Reserved 2021