Does a point in geometry (cartesian and euclidean) occupy space or have volume

Does a point in geometry (cartesian and euclidean) occupy space or have volume

Does a point in geometry (cartesian and euclidean) occupy space or have volume (if we consider 3-D geometry)? And is a line segment always perpendicular to its point of origin? Or can we frame this as, is a line perpendicular to each and every point lying on it?

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