Question

Consider a parallelogram whose sides are represented by the lines $2x+3y=0;2x+3y-5=0$ , $3x-4y=0$ and $3x-4y=3.$ The equation of the diagonal not passing through the origin, is

• A. $21x-11y+15=0$
• B. $9x-11y+15=0$
• C. $21x-29y-15=0$
• D. $21x-11y-15=0$

Answer 1

The correct option is D $21x-11y-15=0$

Let $AB\Rightarrow 2x+3y=0$

$BC\Rightarrow 3x-4y=0$

$CD\Rightarrow 2x+3y-5=0$

$AD\Rightarrow 3x-4y=3$

And considering $B$ to be origin

So, $A\equiv$ solution of $AB$ and $AD$

so, $A\equiv (\frac{9}{17},\frac{-6}{17})$

and $C\equiv$ solution of $BC$ and $CD$

so, $C\equiv (\frac{20}{17},\frac{15}{17})$

So, Equation of $AC$ will be a follows :-

$(y-\frac{15}{17})=\left(\frac{\frac{15}{17}-\left(\frac{-6}{17}\right)}{\frac{20}{17}-\frac{9}{17}}\right)\times (x-\frac{20}{17})$

i.e, $21x-11y-15=0$

Hence, this is the answer.