How to calculate the distance between two points in projective plane

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I have two homogeneous coordinates and I am trying to preserve the distance between two coordinates after various affine trasnformations. Should I calculate the angle between two points ? If so what is the formula to calculate the angle between two points or is there a distance formula other than the general euclidean plane? I found that euclidean distance formula will not preserve the distances

what is the distance formula between two homogeneous coordinates