What is the condition for two lines to be perpendicular?

Two lines with slopes m₁ and m₂ are perpendicular if m₁ × m₂ = −1. For a horizontal line (m₁ = 0), the perpendicular is a vertical line.

How do you find the distance from a point to a line?

For point (x₁, y₁) and line ax + by + c = 0, distance = |ax₁ + by₁ + c| / √(a² + b²). Always use the absolute value in the numerator.

What is intercept form of a line?

x/a + y/b = 1, where a is the x-intercept (where line cuts x-axis) and b is the y-intercept. This form is used when the intercepts are directly given or to be found.

Equation of a Line

Straight Lines • Class 11 Mathematics • NCERT • CBSE

Slope m = (y₂−y₁)/(x₂−x₁). Slope-intercept form: y = mx + c. Point-slope form: y−y₁ = m(x−x₁). Two-point form: (y−y₁)/(y₂−y₁) = (x−x₁)/(x₂−x₁). Distance from point (x₁,y₁) to line ax+by+c=0: |ax₁+by₁+c|/√(a²+b²).

Key Formulas

m = (y₂−y₁)/(x₂−x₁) = tanθ
y = mx + c (slope-intercept)
y−y₁ = m(x−x₁) (point-slope)
x/a + y/b = 1 (intercept form)
d = |ax₁+by₁+c| / √(a²+b²)
m₁ × m₂ = −1 (perpendicular lines)

Frequently Asked Questions

What is the condition for two lines to be perpendicular?: Two lines with slopes m₁ and m₂ are perpendicular if m₁ × m₂ = −1. For a horizontal line (m₁ = 0), the perpendicular is a vertical line.
How do you find the distance from a point to a line?: For point (x₁, y₁) and line ax + by + c = 0, distance = |ax₁ + by₁ + c| / √(a² + b²). Always use the absolute value in the numerator.
What is intercept form of a line?: x/a + y/b = 1, where a is the x-intercept (where line cuts x-axis) and b is the y-intercept. This form is used when the intercepts are directly given or to be found.

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