Mathematics - Area Under Curves Question with Solution | TestHub

$$\begin{array}{l}{x}^2-2xy-xy+2y^2=0\\ \Rightarrow (x-2y)(x-y)=\mathrm{0...}(i)\\ \Rightarrow x=2y,x=y...(ii)\end{array}$$ Also, $x+y+1=0$ On solving Eqs. (i) and (ii), we get (ii) $$\begin{array}{l}A\left(-\frac{2}{3},-\frac{1}{3}\right),B\left(-\frac{1}{2},-\frac{1}{2}\right),C(0,0)\\ \therefore \text{ Area of }△ABC=\frac{1}{2}\left|\begin{array}{rrr}-\frac{2}{3}& -\frac{1}{3}& 1\\ 1& -\frac{1}{2}& 1\\ 0& 0& 1\end{array}\right|\\ =\frac{1}{2}\left[\frac{1}{3}-\frac{1}{6}\right]=\frac{1}{2}\left[\frac{1}{6}\right]=\frac{1}{12}\end{array}$$