Straight Lines And Pair Of Straight Lines

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 :