"My question, can you have lines cross with only three points?"

Lines don't

Lines don't

**end**at points. Three non-linear points typically define a triangle. But if one extends any two of the adjacent line segments that form the sides of the triangle then one has two lines crossing. Unfortunately, by extending the third side (line segment) of the triangle also, one generates in that way**three**points at which two lines cross. So.......... Never mind.
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