Question

The diagonals $AC$ and $BD$ of a rhombus intersect at $(5,6)$. If $A\equiv (3,2)$ then equation of diagonal $BD$ is

• A. $y-x=1$
• B. $2y-x=17$
• C. $y-2x+4=0$
• D. $2y+x=17$

Answer 1

The correct option is D $2y+x=17$

$AO\perp BC$

Slope of $AO=\frac{6-2}{5-3}=\frac{4}{2}=2$

$\therefore$ Slope of $BD=\frac{-1}{2}$

Also, $BO$ passes through $(5,6)$

$\therefore$ Equation of $BD\to (y-6)=\frac{-1}{2}(x-5)$

$\Rightarrow 2y-12=-x+5$

$\Rightarrow x+2y=17.$

Hence, the answer is $x+2y=17.$