Chapter 9 — Straight Lines

Straight lines are fundamental geometric figures in coordinate geometry, defined algebraically through slope-intercept, point-slope, or intercept forms, enabling analysis of parallelism, perpendicularity, and distance relationships.

Chapter 9 covers coordinate geometry's foundational concept of straight lines. Built on distance formulas and section formulae from earlier classes, the chapter systematizes line representation through slope (m = tan θ), where θ is inclination angle. Key topics include slope calculation from two points (m = (y₂ - y₁)/(x₂ - x₁)), conditions for parallelism (equal slopes) and perpendicularity (m₁m₂ = -1), angle between intersecting lines, and multiple equation forms: point-slope (y - y₀ = m(x - x₀)), two-point form, slope-intercept (y = mx + c), and intercept form (x/a + y/b = 1). The chapter concludes with perpendicular distance calculations from a point to a line (d = |Ax₁ + By₁ + C|/√(A² + B²)) and distance between parallel lines.

1. 01Slope m = tan θ measures line inclination; undefined for vertical lines (θ = 90°)
2. 02Slope from two points: m = (y₂ - y₁)/(x₂ - x₁) works for acute and obtuse angles
3. 03Parallel lines have equal slopes; perpendicular lines have slopes satisfying m₁m₂ = -1
4. 04Equation forms: point-slope y - y₀ = m(x - x₀), two-point, slope-intercept y = mx + c, intercept x/a + y/b = 1
5. 05Perpendicular distance from point (x₁,y₁) to line Ax + By + C = 0: d = |Ax₁ + By₁ + C|/√(A² + B²)