The area of the triangle formed by two rays whose combined equation is y = |x| and the line x + 2 y = 2 is

Given Equation y = |x|

$\begin{array}{l}\Rightarrow y=x--\left(1\right)\\ y=-x--\left(2\right)\\ andx+2y=2--\left(3\right)\\ Sub\left(1\right)in\left(3\right)\Rightarrow 3x=2\Rightarrow x=\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.\\ \therefore Thepo\mathrm{int}ofInter\sec tion=\left(\frac{2}{3},\frac{2}{3}\right)\\ Sub\left(2\right)in\left(3\right)\Rightarrow -x=2\Rightarrow x=-2\\ \therefore TheP.I=\left(-2,2\right)\\ P.Iof\left(1\right)\&\left(2\right)is\left(0,0\right)\\ \therefore O\left(0,0\right)A\left(\frac{2}{3},\frac{2}{3}\right)B\left(-2,2\right)\\ Areaof{\Delta }^{le}OAB=\frac{1}{2}\left|x_1{y}_2-x_2{y}_1\right|\\ \Rightarrow \frac{1}{2}\left|\frac{2}{3}\left(2\right)+2\left(\frac{2}{3}\right)\right|\\ \Rightarrow \frac{1}{2}\left|\frac{8}{3}\right|=\frac{4}{3}\end{array}$