It seems that only one can be found, and the X-Y axis of AB intersection can be extended to point C and point D, and the coordinates of point C and point D can be obtained through analytical formula.

Assuming that AB is an edge of a parallelogram, it is only possible if AB∨MN. According to the analytical formula, C, D and O form an isosceles right triangle. Because of parallelism, the angle OMN = 45°, so △OMN is also an isosceles right triangle. According to the properties of parallelogram, AB=MN= radical number 2, so m is (1, 0)N is (0, 1), and then the analytical formula is obtained.

If AB is diagonal, this is impossible.

I hope to adopt. .