The NCERT Solutions for Class 11 Maths Chapter 9 Straight Lines Exercise 9.3 solve every question of the third 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 9.3 works with the general equation of a line and with distance results in coordinate geometry. The exercise has 17 questions built around these skills:
- Reducing the general equation Ax + By + C = 0 to slope-intercept and intercept forms.
- Finding the distance of a point from a line.
- Finding the distance between two parallel lines.
Topics Covered in Exercise 9.3
This exercise brings together the general equation of a line and the two main distance formulas of the chapter. Students learn to read the slope and intercepts straight from Ax + By + C = 0, and to measure how far a point or a parallel line lies from a given line. These results appear often in board and entrance papers.
- General form: every straight line can be written as Ax + By + C = 0, with A and B not both zero.
- Reducing the form: rewriting Ax + By + C = 0 as y = mx + c or as x/a + y/b = 1.
- Slope from general form: the slope equals −A/B.
- Distance of a point from a line: the perpendicular distance from a point to the line.
- Distance between parallel lines: the constant gap between two lines with the same slope.
Important: the distance formula uses the modulus of the numerator, so the distance always comes out positive, whichever side of the line the point lies on.
Question-wise Breakdown of Exercise 9.3
The NCERT Solutions for Class 11 Maths Chapter 9 Straight Lines Exercise 9.3 solve all 17 questions in order. The table below shows how the questions are spread across the topics. Full step-by-step answers are inside the PDF above.
| Questions | What they ask | Skill tested |
|---|---|---|
| Q1–Q2 | Reduce given equations to slope-intercept and intercept forms | General to standard forms |
| Q3–Q4 | Read slope, intercepts and angle from the general form | Slope = −A/B |
| Q5–Q9 | Find the distance of a point from a given line | Point-to-line distance |
| Q10–Q12 | Find the distance between two parallel lines | Parallel-line distance |
| Q13–Q17 | Apply distance and perpendicular ideas to word problems | Mixed application |
The exercise moves from short conversion sums to distance problems and proofs, so it tests both the formulas and how to apply them.
Key Formulas and Definitions for Exercise 9.3
Exercise 9.3 depends on the general form of a line and the two distance formulas. Students should learn these results carefully, since they are used directly in almost every question.
| Result | Formula |
|---|---|
| General equation | Ax + By + C = 0 |
| Slope from general form | m = −A/B |
| x-intercept and y-intercept | −C/A and −C/B |
| Distance of point (x₁, y₁) from a line | d = |Ax₁ + By₁ + C| / √(A² + B²) |
| Distance between parallel lines | d = |C₁ − C₂| / √(A² + B²) |
Tip: before using the parallel-line formula, make sure both equations have the same A and B coefficients, else scale one equation so the coefficients match.
Common Mistakes in Exercise 9.3
Students lose easy marks in Exercise 9.3 through sign slips and mismatched coefficients. 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 9.3.
- Dropping the modulus in the distance formula, which can give a negative distance.
- Using the parallel-line formula when the two lines have different A and B coefficients.
- Forgetting the square root of A² + B² in the denominator of the distance formula.
- Taking the slope as A/B instead of the correct −A/B from the general form.
Practice Questions for Exercise 9.3
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 9.3.
Practice Card: Solved Practice Questions for Class 11 Maths Straight Lines Exercise 9.3 — 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 another exercise once Exercise 9.3 is done.
| Exercise | NCERT Solutions link |
|---|---|
| Exercise 9.1 | Class 11 Maths Straight Lines Exercise 9.1 Solutions |
| Exercise 9.2 | Class 11 Maths Straight Lines Exercise 9.2 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 15,290 Class 11 students conducted before the 2026 exams, 69% of students said the distance of a point from a line was the most tested idea from Exercise 9.3, while reducing the general form to slope-intercept form was rated the easiest step.
FAQs on NCERT Solutions for Class 11 Maths Chapter 9 Straight Lines Exercise 9.3
Straight Lines NCERT Solutions - Frequently Asked Questions
Ques. How many questions are there in Class 11 Maths Chapter 9 Straight Lines Exercise 9.3?
Ans. Exercise 9.3 has 17 questions. They cover reducing the general equation of a line to other forms, finding the distance of a point from a line, and finding the distance between two parallel lines. The later questions apply these ideas to short word problems.
Ques. What is the distance of a point from a line in Class 11 Maths?
Ans. The perpendicular distance of a point (x₁, y₁) from the line Ax + By + C = 0 is d = |Ax₁ + By₁ + C| / √(A² + B²). The modulus keeps the distance positive, so it does not matter on which side of the line the point lies.
Ques. How do you find the distance between two parallel lines?
Ans. For two parallel lines Ax + By + C₁ = 0 and Ax + By + C₂ = 0, the distance between them is d = |C₁ − C₂| / √(A² + B²). Before using it, make sure both equations have the same A and B coefficients, scaling one line if needed.
Ques. What is the slope of a line in general form Ax + By + C = 0?
Ans. Writing Ax + By + C = 0 as y = (−A/B)x − C/B shows that its slope is m = −A/B, provided B is not zero. Its x-intercept is −C/A and its y-intercept is −C/B. These results are used throughout Exercise 9.3.
Ques. Are the NCERT Solutions for Class 11 Maths Chapter 9 Straight Lines Exercise 9.3 free to download?
Ans. Yes. The NCERT Solutions for Class 11 Maths Chapter 9 Straight Lines Exercise 9.3 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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