Question

If the straight lines $y=4-3x$ , $ay=x+10,2y+bx+9=0$ represents three consecutive sides of a rectangle then the value of $ab$ is

• A. $12$
• B. $6$
• C. $18$
• D. $24$

Answer 1

The correct option is C $18$

$y=4-3x$ is perpendicular with $ay=x+10$

So, $(-3)\times \frac{1}{a}=-1$

$\Rightarrow a=3$

And $ay-x-10=0$ is also perpendicular with $2y+bx+9=0$

So, $\frac{1}{a}\times \frac{-b}{2}=-1$

$\Rightarrow b=2a$

$\Rightarrow b=6$

So, value of $ab$ is $3\times 6=18$