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MATH 01310 · College Geometry

MATH 01310 · Transformations & coordinate geometry

Coordinate proofs

Definition

Place a figure on the coordinate plane strategically, then prove geometric claims with algebra: distance, midpoint, slope, and sometimes vectors.

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Good placement: put a vertex at origin, a side on an axis, use symmetry to reduce variables.

Parallel ↔ equal slopes; perpendicular ↔ negative reciprocal slopes (Euclidean).

Midpoint theorem / varignon-type results are clean in coordinates.

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Attempt each problem first, then open the worked solution.

  1. 1.Prove the diagonals of a parallelogram bisect each other with coordinates.