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Prove existence and uniqueness of midpoints

Question:

Prove existence and uniqueness of midpoints.
Existence and Uniqueness of Midpoints Theorem: If A and B are distinct points, then there exists a unique point M such that M is the midpoint of segment AB.
Definition of midpoint: Let A and B be 2 distinct points. The point M is a midpoint of segment AB if M is between A and B and AM=MB.
M is between A and B: M lie on line AB, and AM+MB = AB

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