Question

Two sides of a rhombus are along the lines, $x - y + 1 = 0$ and $7x - y - 5 = 0$. If its diagonals intersect at $(-1, -2)$, then which one of the following is a vertex of this rhombus ?

• A. (-3 , -9)
• B. (-3 , -8)
• C. $\left( \frac{1}{3} , - \frac{8}{3} \right)$
• D. $\left( - \frac{10}{3} , - \frac{7}{3} \right)$

Answer 1

Answer: (C)

Coordinates of $A \equiv (1, 2)$
$\therefore $ Slope of $AE = 2$
$\Rightarrow $ Slope of $BD = - \frac{1}{2}$
$\Rightarrow $ Eq. of $BD$ is $\frac{y + 2 }{ x +1 } = - \frac{1}{2}$
$\Rightarrow x + 2y + 5 = 0$
$\therefore $ Co-ordinates of $D = \left( \frac{1}{3} , \frac{-8}{3} \right)$