Choose the correct answer from the given four options. One vertex of the equilateral triangle with centroid at the origin and one side as x + y – 2 = 0 is \[\] [Hint: Let ABC be the equilateral triangle with vertex A (h, k) and let D ($ \alpha , \beta $ ) be the point on BC. Then $ \large\frac{2\alpha + h}{3}$$=0 = \large\frac{2\beta + k}{3}$. Also $ \alpha + \beta -2 = 0$ and $ \bigg( \large\frac{k-0}{h-0} \bigg) $$ \times (-1) =-1]$

Question

$\begin {array} {1 1} (A)\;(-1,-1) & \quad (B)\;(2,2) \\ (C)\;(-2, -2) & \quad (D)\;(2,-2) \end {array}$