Question

One diagonal of a square is $-3x-4y+8=0$ and one vertex is $(1,1)$, then the area of square is

• A. $\frac{1}{50}$ sq. unit
• B. $\frac{1}{25}$ sq. unit
• C. $\frac{3}{50}$ sq. unit
• D. $\frac{2}{25}$ sq. unit

Answer 1

The correct option is D $\frac{2}{25}$ sq. unit

$OA=OB=P=\left|\frac{-3-4+8}{\sqrt{3^2+4^2}}\right|=\frac{1}{5}$
Thus Area of square
$=4\times \Delta AOB$
$=4(\frac{1}{2}OA.OB)$
$=4(\frac{1}{2}\times \frac{1}{5}\times \frac{1}{5})$
$=\frac{2}{25}sq.unit$