JEE Math Practice Question

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 $$\triangle A B C$$ is an equilateral triangle. Then, the area of the $$\triangle A B C$$ is :

1. A.$$\frac{10}{\sqrt{3}}$$
2. B.$$2 \sqrt{3}$$
3. C.$$3 \sqrt{3}$$
4. D.$$\frac{8}{\sqrt{3}}$$