← 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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Try this
Attempt each problem first, then open the worked solution.
1.Prove the diagonals of a parallelogram bisect each other with coordinates.