Ch 9 covers coordinate geometry of straight lines comprehensively: slope, various forms of line equations, angle between two lines, parallel and perpendicular conditions, and distance formulas.
Slope m = (y₂−y₁)/(x₂−x₁) = tan θ. Forms: slope-intercept (y=mx+c), point-slope (y−y₁=m(x−x₁)), two-point, intercept form (x/a+y/b=1), and normal form (x cos ω + y sin ω = p).
Parallel lines: m₁ = m₂. Perpendicular lines: m₁ × m₂ = −1. Angle between lines: tan θ = |m₁−m₂|/(1+m₁m₂).
Distance from point (x₁,y₁) to line ax+by+c = 0: d = |ax₁+by₁+c|/√(a²+b²). Distance between parallel lines ax+by+c₁=0 and ax+by+c₂=0: d = |c₁−c₂|/√(a²+b²).
Download: https://ncert.nic.in/textbook/pdf/kemh109.pdf | Complete book: https://ncert.nic.in/textbook/pdf/kemh1ps.zip
Two lines with slopes m₁ and m₂ are perpendicular when m₁ × m₂ = −1. For example, y = 2x and y = −x/2 are perpendicular since 2 × (−1/2) = −1. A horizontal and vertical line are also perpendicular.
Book a Trial + Diagnostic session. Get a personalized Learning Path with clear milestones, tutor match, and a plan recommendation — all within 24 hours.
Book Trial + Diagnostic →