Question

The area of the triangle formed by the lines

Answer 1

Area of triangle formed by the lines $a_{1}x+b_{1}y+c_1=0$, $a_{2}x+b_{2}y+c_2=0$ and $a_{3}x+b_{3}y+c_3=0$ is given by
$\Delta =\frac{1}{2}\left|\begin{array}{ccc}{a}_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_3& c_3\end{array}\right|$
A) Area of triangle formed by the lines $6x^2+xy-y^2=0\Rightarrow 3x-y=0,2x+y=0$
and $x-1=0$
$\Delta =\frac{5}{2}$
B) Area of triangle formed by the lines $x^2+xy-2y^2=0\Rightarrow x-y=0,x+2y=0$
and $y-1=0$
$\Delta =\frac{3}{2}$
C) Area of triangle formed by the lines $xy=0\Rightarrow x=0,y=0$
and $x+y=2$
$\Delta =2$
D) Area of triangle formed by the lines $xy-x-y+1=0\Rightarrow x-1=0,y-1=0$
and $x+y-4=0$
$\Delta =2$