Then the coordinates of point A are (1, 2) and B(-2,-1).

So point A and point B are symmetrical about the straight line y=-x, so ① is correct;

When x y 1, so ② is wrong;

S△AOC=S△BOD, so ③ is correct;

When x > 0, y 1 increases with the increase of x; Y2 decreases with the increase of x, so ④ is wrong.

So choose C.