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The documentation of Point states:

Note this should normally be used indirectly via "point" and friends

Indeed, you can do

point([(1,2),(2,3)])

which returns a Graphics object. Is that what you want?

If you want to do anything else with the points then I would just store them as tuples, e.g.

pts = [(1,2), (2,3)]
pts_plot = points(pts)

With the (stored) plot you can also do other things, e.g.

pts_plot + plot(1+x, (x,1,2))