Question

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

• A. $(0,1)$
• B. $(0,-1)$
• C. $(0,2)$
• D. $(0,\frac{5}{2})$

Answer 1

Answer: (D)

$(0,\frac{5}{2})$

Distance between lines AB and CD = distance between lines AD and BC
$\Rightarrow |\frac{2-2\lambda }{\sqrt{2}}|=|\frac{2\lambda +10}{\sqrt{5}0}|\Rightarrow \lambda =0,\frac{5}{2}$
Therefore, the point is $(0,\frac{5}{2})$