In ΔABC, the coordinates of B are (0,0) AB=2, ∠ABC =π3, and the middle point of BC has coordinates (2,0) the centroid of the triangle is

(2,0) is the midpoint of B(0,0) and C.  Then C has coordinates (4,0). Also, A has coordinates (0+2cosπ/3, 0+2 sinπ/3)≡(1,3). Then the centroid is (5/3, 1/3)