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The two points are the ordered pair of the coordinates of the point.
It's true that a point has no dimensions. But a line has one dimension,
not two.
A plane has two dimensions, a solid has three, and that's about all that
ordinary people can visualize.
It is a fixed reference point in space from which distances are measured.
A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space.
A point has no dimensions. It can be drawn anywhere or marked anywhere.
A point is the one which cannot be measured.