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Two sides of a rhombus ABCD are parallel to lines y = x + 2 and y = 7x + 3. If the diagonals of the rhombus intersect at point (1, 2) and the vertex A is on the y -axis is, then the possible coordinates of A are

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a

0,52

b

0,0

c

0,5

d

0,3

answer is A.

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Detailed Solution

The diagonal of rhombus is parallel to angle bisector of given lines.∴ Diagonals are 2y+x=5 and2x−y=0 ∴  Possible coordinates of A are  0,52 or (0, 0)
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Two sides of a rhombus ABCD are parallel to lines y = x + 2 and y = 7x + 3. If the diagonals of the rhombus intersect at point (1, 2) and the vertex A is on the y -axis is, then the possible coordinates of A are