Q. Two sides of a rhombus ABCD are parallel to y = x + 2 and y = 7x + 3. If the diagonals of the rhombus intersect at (1,2) and the vertex A is on the y axis, find the possible co-ordinates of A.
My soln- let A be (0,h). Also let the plane be an argand plane. So B(say) can be obtained by rotating OA 90 degrees about O( ie pt of intersection of diagonals)
OA = -1 + (h-2)i so OB is i times OA ie -i + (2-h) ie B is ( 2-h, -1)
So equating slope in terms of h to those given, we get only one soln h =5/2
In the book, they have used the fact the diagonal bisecting the included angle of the two sides is parallel to the one bisecting the line represented by the two eqns and they get two solutions h = 5/2 and h = 0.
So why is my method missing a solution btw this is an iit 1985 q
thanks
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UP 0 DOWN 0 0 0
