Home Class 11 Applied Maths Chapter 15: Straight Lines
CBSE Applied Maths (2026-27) Unit VII: Coordinate Geometry Weightage: ~5 Marks in Unit

Chapter 15: Straight Lines

Master coordinate geometry tools, slope formulas, line equation forms, angles between lines, and perpendicular distance formulas.

4 Exercises
CBSE Curriculum Aligned
Interactive Quizzes & Solutions

Chapter Exercises & Topics

Select any exercise to access theory notes, formulas, practice drills, and mini tests.

Exercise 15.1 45 mins

Coordinate Geometry Review

  • Cartesian plane, Distance formula: d = √[(x2-x1)^2 + (y2-y1)^2]
  • Section formula (internal and external division)
  • Coordinates of centroid and area of a triangle
Study Exercise Mini Test
Exercise 15.2 45 mins

Slope of a Line

  • Inclination θ and slope (m = tan θ = (y2-y1)/(x2-x1))
  • Angle between two non-vertical lines: tan θ = |(m2 - m1)/(1 + m1 m2)|
  • Conditions for parallelism (m1 = m2) and perpendicularity (m1 m2 = -1)
Study Exercise Mini Test
Exercise 15.3 45 mins

Various Forms of Equations of a Line

  • Lines parallel to coordinate axes (x = c, y = c)
  • Point-slope form: y - y1 = m(x - x1)
  • Two-point form: y - y1 = ((y2 - y1)/(x2 - x1))(x - x1)
  • Slope-intercept form: y = mx + c
  • Intercept form: x/a + y/b = 1
  • General linear equation: Ax + By + C = 0
Study Exercise Mini Test
Exercise 15.4 45 mins

Distance Formulas

  • Perpendicular distance of a point (x1, y1) from a line: d = |Ax1 + By1 + C| / √(A^2 + B^2)
  • Distance between two parallel lines: d = |C1 - C2| / √(A^2 + B^2)
Study Exercise Mini Test

Chapter 15 Core Formula Sheet

Quick-glance formula revision for examination and numerical problem-solving:

  • $$d = √(x_2 - x_1)^2 + (y_2 - y_1)^2$$
  • $$Section Formula: x = m x_2 + n x_1m+n, \quad y = m y_2 + n y_1m+n$$
  • $$Area = 12|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$$
  • $$m = \tan θ = y_2 - y_1x_2 - x_1$$
  • $$\tan θ = |m_2 - m_11 + m_1 m_2|$$
  • $$L_1 \parallel L_2 \iff m_1 = m_2, \quad L_1 \perp L_2 \iff m_1 m_2 = -1$$
  • $$y - y_1 = m(x - x_1), \quad y = mx + c, \quad xa + yb = 1$$
  • $$Ax + By + C = 0 \implies m = -AB, \; c = -CB$$
  • $$d = |A x_1 + B y_1 + C|√A^2 + B^2$$
  • $$d\parallel = |C_1 - C_2|√A^2 + B^2$$
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