JEE Advance - Mathematics (1985 - No. 22)

Two sides of rhombus $$ABCD$$ are parallel to the lines $$y = x + 2$$ and $$y = 7x + 3$$. If the diagonals of the rhombus intersect at the point $$(1, 2)$$ and the vertex $$A$$ is on the $$y$$-axis, find possible co-ordinates of $$A$$.
(0, 0)
(0, 1)
(0, 5/2)
(1, 2)
(5/2, 0)

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