Vector Derivation of the Midpoint Theorem – Parallel and Half‑Length Proof

Derivation of the Mid‑Point Theorem using vectors In this video we present a clear vector‑based proof of the Mid‑Point Theorem. Starting with a statement of the theorem, we set up a triangle with position vectors, define the midpoints of two sides, and compute the connecting segment as a difference of vectors. By simplifying the expression we show that the segment is parallel to the third side and exactly half its length. A second example with the other pair of midpoints reinforces the method. Viewers will learn how to represent geometric points with vectors, how to use averaging to locate midpoints, and how scalar multiples reveal parallelism and proportional lengths. This approach illustrates the power of vector algebra in plane geometry proofs. Generate your own videos for free at https://eduvids.vercel.app