Straight Lines Class 11 Notes: All Forms of a Line and Distance Formulas

Straight Lines is a formula chapter: know the six forms of a line and three distance formulas and every question becomes a two-line substitution.

Slope

• m = (y₂ − y₁)/(x₂ − x₁) = tan θ
• Parallel: m₁ = m₂; perpendicular: m₁m₂ = −1
• Angle between lines: tan θ = |(m₂ − m₁)/(1 + m₁m₂)|

Forms of a line

Form	Equation
Slope-intercept	y = mx + c
Point-slope	y − y₁ = m(x − x₁)
Two-point	y − y₁ = [(y₂ − y₁)/(x₂ − x₁)](x − x₁)
Intercept	x/a + y/b = 1
Normal	x cos ω + y sin ω = p
General	Ax + By + C = 0; slope = −A/B

Distances

• Point (x₁, y₁) from Ax + By + C = 0: |Ax₁ + By₁ + C|/√(A² + B²)
• Between parallel lines Ax + By + C₁ = 0 and Ax + By + C₂ = 0: |C₁ − C₂|/√(A² + B²)

Solved examples

1. Line through (2, 3) perpendicular to 3x − 4y = 5: slope of given = 3/4 → required slope −4/3 → y − 3 = −4/3(x − 2) → 4x + 3y = 17.

2. Distance of (3, −5) from 3x − 4y − 26 = 0: |9 + 20 − 26|/5 = 3/5.

3. Distance between 3x − 4y + 7 = 0 and 3x − 4y + 5 = 0: 2/5 = 0.4.

4. Line with intercepts 3 and −2: x/3 − y/2 = 1 → 2x − 3y = 6.

Common mistakes

• Using slope = A/B instead of −A/B
• Forgetting the modulus in the distance formula
• Applying the parallel-line distance formula when coefficients are not identical

Related: Sets, Relations and Functions.

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Frequently asked questions

Are these Straight Lines Class 11 Notes notes enough for the exam?

They cover every formula, definition and question type that appears in school and board papers for this chapter. Use them with the NCERT examples, exercise questions and the last five years' papers to be fully prepared.

How should I revise Straight Lines Class 11 Notes?

Revise the notes after 1 day, 7 days and 30 days. Solve five questions each time instead of only reading, and keep an error list of the steps you get wrong.

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