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A point zero dimensional can exist in a to dimensional plane because it occupies the zero point in both dimensions.
Zero. Points are zero dimensional objects. Straight lines are one dimensional objects. Planes and surfaces are two dimensional objects. Volumes and polyhedra are examples of three dimensional objects.
A figure having zero dimensions is a point.
A zero-dimensional shape is a point.
A point has zero dimensions; a line has only one direction, which is length. Two-dimensional objects have length and width, and therefore area.