Step 1 :Reflect the points A = [2, -1], B = [2, -4], C = [4, -2] over the y-axis. This changes the sign of the x-coordinate of each point, resulting in A1 = [-2, -1], B1 = [-2, -4], C1 = [-4, -2].
Step 2 :Translate the points by the vector <2,-1>. This means we add 2 to the x-coordinate and subtract 1 from the y-coordinate of each point, resulting in A2 = [0, -2], B2 = [0, -5], C2 = [-2, -3].
Step 3 :Rotate the points 180 degrees about the origin. This changes the sign of both the x and y coordinates of each point, resulting in A3 = [0, 2], B3 = [0, 5], C3 = [2, 3].
Step 4 :\(\boxed{\text{The final coordinates of the transformed triangle are A' = (0, 2), B' = (0, 5), and C' = (2, 3).}}\)