📐 CBSE · Class 11 · Mathematics · Chapter 10

Straight
Lines

Complete chapter resources for CBSE Class 11 Maths — topic breakdown, key formulas, slope and line equations, distance formulas, sample questions, previous year board questions, and instant AI question paper generation.

4Topics
6–8Board marks
8Sample questions
3PYQ included
Sign Up Free & Generate → See sample questions ↓

Free for independent teachers · No credit card required

Key Formulas — Chapter 10
  • Slope: m = (y₂ − y₁) / (x₂ − x₁)
  • Slope-intercept: y = mx + c
  • Point-slope: y − y₁ = m(x − x₁)
  • Angle between lines: tan θ = |(m₁ − m₂) / (1 + m₁m₂)|
  • Dist. point to line: d = |ax₁ + by₁ + c| / √(a² + b²)
  • Dist. parallel lines: d = |c₁ − c₂| / √(a² + b²)
Chapter Overview

What this chapter covers

Chapter 10 of NCERT Class 11 Mathematics extends the coordinate geometry introduced in earlier classes to a rigorous treatment of straight lines in the Cartesian plane. The chapter begins with the concept of slope (gradient) — the measure of steepness of a line — and establishes how slope is related to the angle a line makes with the positive x-axis. Conditions for two lines to be parallel (equal slopes) or perpendicular (product of slopes = −1) are derived here.

The chapter then systematically develops every standard form of the equation of a straight line: slope-intercept form, point-slope form, two-point form, intercept form (x/a + y/b = 1), and normal form (x cos ω + y sin ω = p). Students also learn how to reduce the general equation ax + by + c = 0 to each of these forms. A major topic is the angle between two intersecting lines and conditions for collinearity of three points.

The chapter closes with the distance formulas — distance from a point to a line, and distance between two parallel lines — which have direct applications in geometry, physics, and engineering problems. Board questions consistently test these formulas in both direct computation and word-problem settings, making them among the highest-value topics in this chapter.

Topics

What's inside Chapter 10

As per NCERT Class 11 Mathematics (CBSE syllabus)

Topic 1
Slope of a Line
Slope as tan of inclination angle. Slope from two points: m = (y₂ − y₁)/(x₂ − x₁). Conditions for parallel lines (m₁ = m₂) and perpendicular lines (m₁ · m₂ = −1). Collinearity of three points.
Topic 2
Equations of a Line — Various Forms
Slope-intercept (y = mx + c), point-slope (y − y₁ = m(x − x₁)), two-point form, intercept form (x/a + y/b = 1), and normal form (x cos ω + y sin ω = p). Reducing the general form ax + by + c = 0 to each standard form.
Topic 3
Angle Between Two Lines
Formula: tan θ = |(m₁ − m₂)/(1 + m₁m₂)|. Finding acute angle between intersecting lines, finding the slope of a line that makes a given angle with another line, and the special cases of parallel and perpendicular lines.
Topic 4
Distance Formulas
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). Applications in triangle geometry.
Connections

How this chapter fits in

Useful for setting question difficulty and cross-chapter papers.

Builds on
Class 10 · Coordinate Geometry
Distance formula, section formula, area of triangle by coordinates
Ch 3 · Trigonometric Functions
Tan of inclination angle, angle between lines derivation
Chapter 10 Straight
Lines
Leads to
Ch 11 · Conic Sections
Lines as degenerate conics; tangent and normal lines to curves
Class 12 · Application of Derivatives
Tangent and normal to curves use straight-line equations directly
Board Blueprint

Marks & question-type breakdown

Typical pattern based on CBSE Class 11 Mathematics papers from the last five years.

Question type Marks Typical count What's usually tested
MCQ / Objective 1 1–2 Slope of a line, condition for parallel/perpendicular, or intercept identification
Very Short Answer 2 1 Equation of a line given slope and point, or angle between two lines
Short Answer 3 1 Reduce general equation to standard form, or find equation satisfying two conditions
Long Answer / Application 4–5 1 Distance from point to line, distance between parallel lines, or triangle area/altitude
Total (approximate) 6–8 4–5 Weightage varies across paper sets and years
Sample Questions

8 sample questions — generated by MarksZen AI

Aligned to CBSE Class 11 Maths Chapter 10. Covers all question types across Easy, Medium, and Hard difficulty.

Q1 Easy 1 mark MCQ
The slope of the line passing through the points (3, −2) and (7, 4) is: (a) 3/2 (b) 2/3 (c) −3/2 (d) −2/3
Q2 Easy 2 marks Short Answer
Find the equation of the line with slope −3 and y-intercept 5. Write the answer in slope-intercept form and in the general form ax + by + c = 0.
Q3 Medium 2 marks Short Answer
Find the angle between the lines y = √3 x + 5 and y = (1/√3) x − 2. Express the answer in degrees.
Q4 Medium 3 marks Short Answer
Reduce the equation 3x − 4y + 8 = 0 to (i) slope-intercept form, (ii) intercept form, and (iii) normal form. State the slope, x-intercept, y-intercept, and the perpendicular distance from the origin in each case.
Q5 Medium 3 marks Short Answer
The line through points A(2, 3) and B(4, k) is perpendicular to the line 3x + 2y = 7. Find the value of k and write the equation of line AB.
Q6 Hard 4 marks Word Problem
Find the distance of the point (3, −5) from the line 3x − 4y + 26 = 0. Also find the foot of the perpendicular from this point to the line.
Q7 Hard 4 marks Word Problem
Find the distance between the parallel lines 8x + 15y − 34 = 0 and 8x + 15y + 51 = 0. A point P lies on the first line. Verify that the distance formula gives the same result as the perpendicular from P to the second line.
Q8 Hard 5 marks Case-Based
The vertices of a triangle are A(1, 3), B(4, −1), and C(−2, 5). (i) Find the equation of the median from vertex A. (ii) Find the equation of the altitude from vertex B. (iii) Find the length of the altitude from B to side AC.
Generate a full paper with answer key →

MarksZen AI creates a complete question paper with answer key in under 2 minutes.

Previous Year Questions

From CBSE board examinations

Actual questions from past Class 11 Maths board papers — Straight Lines chapter.

Board 20224 marks
Find the equation of the line passing through the point (2, 3) and making equal intercepts on the coordinate axes. Also find the distance of this line from the origin. (CBSE 2022)
Board 20233 marks
Find the equation of the line which passes through the point (1, −2) and is perpendicular to the line 4x + 3y − 5 = 0. Also, find the distance between the two parallel lines 4x + 3y − 5 = 0 and 4x + 3y + 15 = 0. (All India 2023)
Board 20204 marks
If the lines 2x + y − 3 = 0, 5x + ky − 3 = 0, and 3x − y − 2 = 0 are concurrent, find the value of k. Hence determine whether the three lines meet at a single point, showing the full method. (CBSE 2020)
For Teachers

Create a board-aligned
question paper in 2 minutes.

Pick chapter, set the question-type mix and total marks — MarksZen AI generates the full paper with answer key. CBSE, ICSE, and all State Boards supported.

  • All 4 topics of this chapter
  • MCQ + short answer + application problems
  • Answer key included
  • PDF export ready
Sign Up Free & Generate →
FAQ

Questions teachers ask

How many marks does Straight Lines carry in the CBSE Class 11 Mathematics exam? +
Straight Lines typically carries 6–8 marks in CBSE Class 11 Mathematics unit tests and annual exams. Questions are spread across 1-mark MCQs (slope or intercept identification), 2-mark short answers (finding the equation of a line), and 4–5 mark problems (distance formulas, angle between lines, or family of lines).
Which form of the equation of a line should students prefer in board exams? +
All standard forms — slope-intercept (y = mx + c), point-slope (y − y₁ = m(x − x₁)), two-point form, intercept form (x/a + y/b = 1), and normal form — are equally valid in CBSE exams. Students should choose the form that fits the given data most directly. The slope-intercept and point-slope forms are the fastest in most contexts; the normal form is mandatory when the perpendicular distance from the origin is given.
What is the formula for the angle between two lines and when is it tested? +
The acute angle θ between two lines with slopes m₁ and m₂ is given by tan θ = |(m₁ − m₂) / (1 + m₁m₂)|. Board questions typically ask students to find the angle between two given lines, or to find the slope of a line that makes a given angle with another line. This is a regular 2–3 mark question in CBSE Class 11 papers.
Are the distance-from-a-point-to-a-line and distance-between-parallel-lines formulas important for boards? +
Yes, both are high-probability board topics. The distance from point (x₁, y₁) to line ax + by + c = 0 is |ax₁ + by₁ + c| / √(a² + b²). The distance between parallel lines ax + by + c₁ = 0 and ax + by + c₂ = 0 is |c₁ − c₂| / √(a² + b²). These typically appear as 2–4 mark questions and are almost certain to feature in at least one question each year.
How do I generate a custom question paper for Straight Lines using MarksZen? +
Sign up for a free MarksZen account, choose CBSE Class 11 Mathematics, select Chapter 10 (Straight Lines), set your preferred question-type mix (MCQ, short answer, word problem) and total marks — the AI generates a complete board-aligned paper with answer key in under 2 minutes, ready for PDF export.