2D Coordinates of point defined as fractions of rectangular sides. Rectangular is not parallel to X, Y axes

I have a rectangular ABCD: (x1,y1)... (x4,y4). AB is not necessarily parallel to any of the axis.

I need to find coordinates of a point inside of it, defined as portion of its sides: alpha *AB, alpha*CD . beta*BC, beta*DA. where alpha and beta are between 0 and 1.

Is there as simple solution to it?

source https://stackoverflow.com/questions/76894736/2d-coordinates-of-point-defined-as-fractions-of-rectangular-sides-rectangular-i

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