G GPE A 1 Worksheet 3 Coordinate Geometry Proofs and Calculations Guide

Confirm each result by recalculating distance, slope, midpoint using exact formulas. Every task here relies on the distance formula, midpoint rule, or slope comparison, applied directly to given coordinate pairs.

Check segment congruence by matching squared distances, not rounded values. Parallel lines require equal slopes, while perpendicular lines depend on negative reciprocal slopes. Write each step clearly to avoid sign errors.

Several problems combine algebra and geometry. Simplify expressions before substitution, keep variables aligned to axes, and verify symmetry across midpoints when shapes share properties.

Use these worked solutions for self review after class practice. Compare your process line by line, flag repeated calculation slips, and adjust your setup for future coordinate proofs.