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A point zero dimensional can exist in a to dimensional plane because it occupies the zero point in both dimensions.
Yes
A figure having zero dimensions is a 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.
A point has zero dimensions; a line has only one direction, which is length. Two-dimensional objects have length and width, and therefore area.