Key Concepts: Proofs in Coordinate Geometry ⭐

Coordinate Proofs

A coordinate proof uses the coordinate Plane and algebraic methods (distance formula, midpoint formula, slope) to prove geometric theorems.

Steps for Coordinate Proofs

1. Place the figure in the coordinate Plane (choose convenient coordinates).
2. Use the Distance Formula to find lengths.
3. Use the Midpoint Formula to find midpoints.
4. Use the Slope Formula (rise/run) to determine parallelism or perpendicularity.
5. Draw conclusions based on the calculations.

Slope

slope = (y₂ − y₁) / (x₂ − x₁)

• Parallel lines have equal slopes.
• Perpendicular lines have slopes that are negative reciprocals (product = −1).