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 $D=\left(\frac{1}{3},\frac{-8}{3}\right)$