Coordinate Geometry
Cartesian plane: x-axis (horizontal), y-axis (vertical), origin (0, 0).
Slope: m = (y₂ − y₁) / (x₂ − x₁). Positive = rises left to right. Negative = falls. Zero = horizontal. Undefined = vertical.
Slope-intercept form: y = mx + b (m = slope, b = y-intercept)
Parallel lines: same slope. Perpendicular lines: slopes are negative reciprocals (m₁ × m₂ = −1).
Distance formula: d = √[(x₂ − x₁)² + (y₂ − y₁)²]
Midpoint formula: M = ((x₁ + x₂)/2, (y₁ + y₂)/2)