Question

The diagonals of a rhombus ABCD intersect at the point (1, 2) and its sides are parallel to the lines x –√3y + 2√3 = 0 and √3x - y + 3 = 0.If the vertex A be situated on x-axis, then possible co-ordinates of vertex C are

(A)  (1, 4) and (– 3, 4)

(B)  (–1, –4) and (– 3, –4)

(C)  (– 1, 4) and (3, 4)

(D)  None of these 

Answer 1

Correct option (C) (– 1, 4) and (3, 4)

Equation of diagonal A may be 

y - 2 = ± (x - 1)

⇒ y = x + 1 or y = -x + 3

⇒ Vertex A may be (-1, 0) or (3, 0)

Also, length of diagonal AC in both cases is 4√2

Now, if A ≡ (-1, 0), then vertex C will be

Also, if A ≡ (3, 0), then vertex C will be