One-point perspective has only one vanishing point.
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Two points are sufficient.
one point can form a line! horizontally or vertically... but a line doesn't need any points.
exactly three times as far from point A as they are from point B?
No, they can intersect at infinitely many points.
two points form a line one more point is needed to check whether it is collinear or not so atleast three points must be require to check the non collinerancy of a points