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Technically they don't because the definition of a point is a specific place of a certain object in a graph, and you could keep cutting up the point infinity times and still not have the most exact location as possible. Thus, a point can be any shape, but for a point there will never be an exact location or a definite size or shape. Most points in geometry are little circles such as on a line graph, but a point could be a square. A point is just the most exact location of something in a geometry problem. That's all it is.

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Q: Do points have a definite shape in geometry?
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