Question

Two sides of a rectangle are $3x+4y+5=0$,$-4x+3y+15=0$ and its one vertex is $(0,0)$. Then the area of the rectangle is

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

Answer: (B)

$3$

As $(0,0)$ Does not lies on $3x+4y+5=0,4x+3y+15=0$
Perpendicular distance from $(0,0)$ to $3x+4y+5=0$ is
$A=\left|\frac{3.0+4.0+5}{\sqrt{3^2+4^2}}\right|=1$
And perpendicular distance from $(0,0)$ to $4x+3y+15=0$ is
$B=\left|\frac{4.0+3.0+15}{\sqrt{4^2+3^2}}\right|=3$
Then area as $AB=1\times 3=3$ sq. units.