Let B and C be the two points on the line y+x=0 such that B and C are symmetric with respect to the origin. Suppose A is a point on y-2 x=2 such that…

Let $\displaystyle B$ and $\displaystyle C$ be the two points on the line $\displaystyle y+x=0$ such that $\displaystyle B$ and $\displaystyle C$ are symmetric with respect to the origin. Suppose $\displaystyle A$ is a point on $\displaystyle y-2 x=2$ such that $\displaystyle \triangle A B C$ is an equilateral triangle. Then, the area of the $\displaystyle \triangle A B C$ is