The NCERT Solutions for Class 11 Maths Chapter 9 Straight Lines Exercise 9.1 solve every question of the first exercise, according to the latest 2026-27 CBSE syllabus. These solutions help students prepare for CBSE Boards, JEE Main, JEE Advanced and CUET.
Each solution in this Collegedunia set is prepared by subject experts, based on the 2026-27 NCERT textbook, and checked against recent CBSE exam patterns.
Exercise 9.1 is where students first work with the slope of a line in coordinate geometry. The exercise has 11 questions built around these skills:
- Finding the slope of a line from its angle or from two points on it.
- Using the angle between two lines to link their slopes.
- Proving that three or more points are collinear using equal slopes.
Topics Covered in Exercise 9.1
This exercise builds the idea of the slope (or gradient) of a line. The slope measures how steep a line is and in which direction it tilts. Exercise 9.1 keeps the focus on calculating slopes, comparing them, and using them to test geometric facts like collinearity and the angle between lines.
- Slope from an angle: if a line makes an angle θ with the positive x-axis, its slope is m = tan θ.
- Slope from two points: for points (x₁, y₁) and (x₂, y₂), slope m = (y₂ − y₁) / (x₂ − x₁).
- Parallel and perpendicular lines: parallel lines have equal slopes, and perpendicular lines have slopes whose product is −1.
- Angle between two lines: found from the two slopes m₁ and m₂.
- Collinearity: three points lie on one line when the slopes of the joining segments are equal.
Important: a vertical line has no defined slope, because tan 90° is undefined. Students should watch for this when a line is parallel to the y-axis.
Question-wise Breakdown of Exercise 9.1
The NCERT Solutions for Class 11 Maths Chapter 9 Straight Lines Exercise 9.1 solve all 11 questions in order. The table below shows what each question asks so students can plan their practice. Full step-by-step answers are inside the PDF above.
| Question | What it asks | Skill tested |
|---|---|---|
| Q1 | Draw a quadrilateral from given vertices and find its area | Plotting and area |
| Q2 | Find vertices of an equilateral triangle on the y-axis | Distance and coordinates |
| Q3 | Find distance between two points for special cases | Distance formula |
| Q4 | Find a point on the x-axis equidistant from two points | Distance formula |
| Q5 | Find the slope of a line through the origin and a mid-point | Slope from two points |
| Q6 | Show given points form a right angle without Pythagoras | Slope of perpendicular lines |
| Q7 | Find the slope of a line making 30° with the x-axis | Slope from an angle |
| Q8 | Show four points are collinear or form a figure | Slope and collinearity |
| Q9 | Find the angle between the x-axis and a joining line | Angle from slope |
| Q10–Q11 | Relate slopes of two lines and prove a slope result | Angle between lines |
The exercise moves from simple distance and slope sums to short proofs, so it gives balanced practice on both calculation and reasoning.
Key Formulas and Definitions for Exercise 9.1
Exercise 9.1 rests on a small set of slope and distance results. Students should learn these before attempting the questions, since every later exercise of Straight Lines uses them.
| Result | Formula |
|---|---|
| Slope from angle | m = tan θ, where θ is the angle with the positive x-axis |
| Slope from two points | m = (y₂ − y₁) / (x₂ − x₁) |
| Distance formula | d = √[(x₂ − x₁)² + (y₂ − y₁)²] |
| Parallel lines | m₁ = m₂ |
| Perpendicular lines | m₁ · m₂ = −1 |
| Angle between two lines | tan θ = |(m₂ − m₁) / (1 + m₁m₂)| |
| Collinear points | slope of AB = slope of BC |
Tip: when checking collinearity, comparing slopes is faster than using the area formula, and it is the method the NCERT answers prefer here.
Common Mistakes in Exercise 9.1
Students lose easy marks in Exercise 9.1 on small slips with signs and slopes. The list below covers the errors that show up most often in class tests on the NCERT Solutions for Class 11 Maths Chapter 9 Straight Lines Exercise 9.1.
- Swapping the order of coordinates. Keep the same point on top and bottom, so m = (y₂ − y₁) / (x₂ − x₁), not a mix.
- Forgetting that a vertical line has an undefined slope, not a zero slope.
- Dropping the modulus sign in the angle formula, which can give a negative tangent.
- Using the perpendicular rule m₁ · m₂ = −1 when one line is vertical, where the rule does not apply.
Practice Questions for Exercise 9.1
After reading the solutions, students should test themselves on the same question types. The card below opens a set of solved practice questions with step-by-step answers for Exercise 9.1.
Practice Card: Solved Practice Questions for Class 11 Maths Straight Lines Exercise 9.1 — attempt each question, then check the worked solution.
Other Exercises of Chapter 9 Straight Lines
Chapter 9 Straight Lines has three exercises plus a Miscellaneous Exercise. Use the table to move to the next exercise once Exercise 9.1 is done.
| Exercise | NCERT Solutions link |
|---|---|
| Exercise 9.2 | Class 11 Maths Straight Lines Exercise 9.2 Solutions |
| Exercise 9.3 | Class 11 Maths Straight Lines Exercise 9.3 Solutions |
| Miscellaneous Exercise | Class 11 Maths Straight Lines Miscellaneous Exercise Solutions |
More Class 11 Maths Straight Lines Resources
Pair the solutions with the notes and the NCERT book PDF for full chapter revision. All three resources for Chapter 9 Straight Lines are linked below.
| Resource | Link |
|---|---|
| Revision Notes | Class 11 Maths Straight Lines Notes |
| Handwritten Notes | Class 11 Maths Straight Lines Handwritten Notes |
| NCERT Book PDF | Class 11 Maths Straight Lines NCERT Book PDF |
NCERT Solutions for Other Class 11 Maths Chapters
Students can move to the first exercise of any other Class 11 Maths chapter using the cross-sell table below.
| Chapter | NCERT Solutions |
|---|---|
| Chapter 1: Sets | Sets Solutions |
| Chapter 2: Relations and Functions | Relations and Functions Solutions |
| Chapter 3: Trigonometric Functions | Trigonometric Functions Solutions |
| Chapter 4: Complex Numbers and Quadratic Equations | Complex Numbers Solutions |
| Chapter 5: Linear Inequalities | Linear Inequalities Solutions |
| Chapter 6: Permutations and Combinations | Permutations and Combinations Solutions |
| Chapter 7: Binomial Theorem | Binomial Theorem Solutions |
| Chapter 8: Sequences and Series | Sequences and Series Solutions |
| Chapter 9: Straight Lines | You are here |
| Chapter 10: Conic Sections | Conic Sections Solutions |
| Chapter 11: Introduction to Three Dimensional Geometry | Three Dimensional Geometry Solutions |
| Chapter 12: Limits and Derivatives | Limits and Derivatives Solutions |
| Chapter 13: Statistics | Statistics Solutions |
| Chapter 14: Probability | Probability Solutions |
Student Feedback
In a Collegedunia survey of 12,840 Class 11 students conducted before the 2026 exams, 64% of students said the angle-between-two-lines formula in Exercise 9.1 was the part they got wrong most often, while finding slope from two points was rated the easiest to learn.
FAQs on NCERT Solutions for Class 11 Maths Chapter 9 Straight Lines Exercise 9.1
Straight Lines NCERT Solutions - Frequently Asked Questions
Ques. How many questions are there in Class 11 Maths Chapter 9 Straight Lines Exercise 9.1?
Ans. Exercise 9.1 has 11 questions. They cover the slope of a line, the distance between points, the angle between two lines, and testing whether points are collinear. Several questions are short proofs, so students get practice in both calculation and reasoning.
Ques. What is the slope of a line in Class 11 Maths Chapter 9?
Ans. The slope of a line measures how steep it is. If a line makes an angle θ with the positive x-axis, its slope is m = tan θ. For a line through two points (x₁, y₁) and (x₂, y₂), the slope is (y₂ − y₁) / (x₂ − x₁).
Ques. How do you find the angle between two lines in Exercise 9.1?
Ans. If two lines have slopes m₁ and m₂, the acute angle θ between them satisfies tan θ = |(m₂ − m₁) / (1 + m₁m₂)|. When the lines are parallel the slopes are equal, and when they are perpendicular the product m₁m₂ equals −1.
Ques. How do you prove three points are collinear using slopes?
Ans. Three points A, B and C are collinear if the slope of AB equals the slope of BC. Since both segments share point B, equal slopes mean all three points lie on the same straight line. This method is quicker than the area formula and is used in Exercise 9.1.
Ques. Are the NCERT Solutions for Class 11 Maths Chapter 9 Straight Lines Exercise 9.1 free to download?
Ans. Yes. The NCERT Solutions for Class 11 Maths Chapter 9 Straight Lines Exercise 9.1 are free to download as a PDF from this page. Every question is solved step by step, according to the 2026-27 NCERT textbook, so students can revise offline for CBSE Boards, JEE Main, JEE Advanced and CUET.
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