Area of the parallelogram whose sides are $2 x+y+1=0,2 x+y+4=0, x-3 y-1=0$ and $x-3 y+2=0$ is equal

Question

Area of the parallelogram whose sides are $2 x+y+1=0,2 x+y+4=0, x-3 y-1=0$ and $x-3 y+2=0$ is equal to

Professor PC Thomas Classes · Answer

Area of parallelogram bounded by $a_1x+b_1y+c_1=0$, etc is $\frac{|(c_1-c_2)(d_1-d_2)|}{|a_1b_2 - a_2b_1|}$. $A = \frac{|(1-4)(-1-2)|}{|-6-1|} = \frac{9}{7}$.