<Qua-2025-770>, HINT 

Let a,b,c,d be the x-coordinates of point A,B,C,D and

A',B',C',D' be the x-coordinates of points A',B',C',D'

(A'+a)/2=b ---> A'=2b-a, B'=2c-b, C'=2d-c, D'=2a-d, Add up all

A'+B'+C'+D'=a+b+c+d. Suppose above origin (0,0)

C'+2D'=4a-c   A'+2B'=4c-a by arranging  15a=A'+2B'+4C'+8D'

Similarly b,c,d are defined with given A',B',C',D'.