India's #1 AI Tutorworksheet · Mathematics · Chapter 3

CBSE Class 9 Mathematics Chapter 3 Coordinate Geometry Worksheet with Answers

Coordinate Geometry is a foundational chapter in CBSE Class 9 Mathematics that bridges algebra and geometry by representing points on a plane using ordered pairs. This worksheet is designed for focused practice, covering the full spectrum of question types that appear in CBSE examinations—from objective MCQs to case-based reasoning. With a suggested time of 90 minutes and medium difficulty, it serves as an excellent tool for self-assessment and revision before term exams.

Your child's private AI tutor — trained on NCERT.

3-day free trial · ₹1 to start · Cancel anytime.

Start 3-day free trial →

Key takeaways

✓Coordinate Geometry introduces the Cartesian plane, with x-axis and y-axis dividing it into four quadrants for plotting points and understanding relationships.
✓The origin (0, 0) is the intersection point of the axes; x-coordinate (abscissa) measures horizontal distance, y-coordinate (ordinate) measures vertical distance.
✓Signs of coordinates change across quadrants: (+, +) in I, (−, +) in II, (−, −) in III, and (+, −) in IV.
✓Distance formula and section formula are Class 10 extensions; Class 9 focuses on plotting, identifying quadrants, and understanding basic coordinate concepts.
✓Real-world applications include map reading, GPS coordinates, graphing data, and locating objects in a plane using ordered pairs.
✓This worksheet covers all NCERT exercise patterns and includes HOTS questions for competitive exam readiness and deeper conceptual clarity.
✓Complete answer key with explanations helps self-assessment and builds confidence for CBSE term exams and internal assessments.

Quick Chapter Recap: Coordinate Geometry Essentials

Coordinate Geometry, also known as Cartesian Geometry, was developed by René Descartes to describe the position of points in a plane. The Cartesian plane consists of two perpendicular number lines: the horizontal x-axis and the vertical y-axis. Their intersection is the origin, denoted O(0, 0). Any point P in the plane is represented by an ordered pair (x, y), where x is the abscissa (distance from the y-axis) and y is the ordinate (distance from the x-axis). The plane is divided into four quadrants: Quadrant I (both coordinates positive), Quadrant II (x negative, y positive), Quadrant III (both negative), and Quadrant IV (x positive, y negative). Points on the axes are not considered to belong to any quadrant. Class 9 NCERT Chapter 3 emphasizes plotting points, understanding the sign convention, and applying coordinate concepts to simple problems. Mastery of this chapter prepares students for advanced topics like distance formula, section formula, and area of triangles in Class 10.

Origin (0, 0) is the reference point for all coordinates in the plane.
Abscissa (x-coordinate) is always written first, ordinate (y-coordinate) second in the ordered pair.
Perpendicular distance from the x-axis gives the y-coordinate; from the y-axis gives the x-coordinate.
Points on the x-axis have y-coordinate 0; points on the y-axis have x-coordinate 0.
Reflection of point (x, y) across the x-axis is (x, −y); across the y-axis is (−x, y).

Section A: Multiple Choice Questions (1 mark each)

Multiple-choice questions test your ability to quickly recall definitions, sign conventions, and quadrant properties. In CBSE Class 9 Mathematics Chapter 3, MCQs often ask about identifying quadrants, recognizing coordinates of specific points, or applying basic coordinate rules. Each question below has four options; select the most appropriate one. These questions mirror the pattern seen in CBSE sample papers and NCERT exemplar problems. Practicing MCQs sharpens decision-making speed and accuracy, both critical for scoring well in objective sections of term exams. Pay close attention to the signs of coordinates and the position of points relative to the axes. Remember that points on axes do not belong to any quadrant, a common trap in MCQs. Attempting these under timed conditions simulates exam pressure and builds confidence.

Q1. The point (−5, 2) lies in which quadrant? (A) I (B) II (C) III (D) IV
Q2. The abscissa of a point on the y-axis is: (A) 0 (B) 1 (C) Any positive number (D) Any negative number
Q3. If a point lies in Quadrant III, its coordinates are of the form: (A) (+, +) (B) (−, +) (C) (−, −) (D) (+, −)
Q4. The coordinates of the origin are: (A) (1, 1) (B) (0, 1) (C) (1, 0) (D) (0, 0)
Q5. The point (0, −7) lies on: (A) x-axis (B) y-axis (C) Quadrant III (D) Quadrant IV
Q6. The mirror image of point (4, 3) in the x-axis is: (A) (−4, 3) (B) (4, −3) (C) (−4, −3) (D) (3, 4)

Section B: Fill in the Blanks (1 mark each)

Fill-in-the-blank questions require precise terminology and numerical accuracy. They test whether you understand key vocabulary like abscissa, ordinate, origin, and quadrant without the aid of options. In CBSE Class 9 Mathematics Chapter 3, these questions often focus on coordinate definitions, axis properties, and sign conventions. Write your answers clearly and check spelling, especially for terms like abscissa and ordinate, which are frequently misspelled. This section builds conceptual clarity because you must retrieve the exact term or number from memory. It also reinforces the language of coordinate geometry, which is essential for writing clear explanations in long-answer questions. Practice these blanks by covering the answer key and attempting them independently, then verify your responses to identify gaps in understanding.

Q7. The horizontal number line in the Cartesian plane is called the __________.
Q8. The y-coordinate of a point is also known as the __________.
Q9. A point with coordinates (0, 0) is called the __________.
Q10. In Quadrant IV, the x-coordinate is __________ and the y-coordinate is __________.
Q11. The perpendicular distance of a point from the y-axis is its __________.

Section C: True or False (1 mark each)

True or false questions are deceptively simple but demand careful reading and understanding of coordinate geometry principles. A single misplaced sign or overlooked word can lead to an incorrect answer. These questions often test subtle distinctions, such as whether a point on an axis belongs to a quadrant, or the effect of changing the sign of one coordinate. In the CBSE Class 9 Mathematics Chapter 3 context, true/false items reinforce core concepts and challenge common misconceptions. Always justify your answer mentally or in rough work before marking true or false; this habit prevents careless errors. These questions also prepare you for assertion-reason type questions introduced in higher classes. Pay attention to absolute statements (using words like always, never, all) which are often false unless the condition is universally true.

Q12. The point (5, 0) lies on the x-axis. True / False
Q13. The coordinates of a point in Quadrant II are both negative. True / False
Q14. The ordinate of every point on the x-axis is zero. True / False
Q15. The point (−3, −3) lies in Quadrant III. True / False
Q16. Reflection of (a, b) in the y-axis is (a, −b). True / False

Section D: Short Answer Questions (2 marks each)

Short-answer questions in CBSE Class 9 Mathematics Chapter 3 Coordinate Geometry typically require plotting points, identifying quadrants, or applying coordinate concepts in one or two logical steps. Each question is worth 2 marks, so write concise yet complete answers. Show your working clearly, especially when calculating or reasoning about signs. These questions assess both procedural fluency (can you plot a point correctly?) and conceptual understanding (do you know why a point lies in a particular quadrant?). Practice drawing neat Cartesian planes with properly labeled axes and origin. Use a ruler for accuracy. Marks are often deducted for unlabeled diagrams or incorrect scales. This section bridges the gap between objective questions and longer HOTS problems, building the skills needed for comprehensive answers in Section E.

Q17. Plot the points A(2, 3), B(−1, 4), and C(−3, −2) on a Cartesian plane and state the quadrant in which each lies.
Q18. Write the coordinates of any two points that lie on the y-axis.
Q19. If the abscissa of a point is −4 and its ordinate is 0, where does the point lie?
Q20. Find the coordinates of the reflection of the point (3, −5) in the x-axis.
Q21. A point lies in Quadrant II and is equidistant from both axes. If its distance from each axis is 6 units, what are its coordinates?

Section E: Long Answer and HOTS Questions (3-5 marks each)

Long-answer questions demand multi-step reasoning, clear explanations, and sometimes the integration of coordinate geometry with other mathematical concepts. Higher Order Thinking Skills (HOTS) questions test your ability to apply coordinate concepts in unfamiliar or complex scenarios. In CBSE Class 9 Mathematics Chapter 3, long-answer questions might involve plotting multiple points, identifying patterns, or reasoning about geometric shapes on the coordinate plane. Allocate 5-7 minutes per question. Start by reading the question twice to understand what is being asked. Draw diagrams wherever possible; visual representation often reveals the solution path. Show every step of your working; partial marks are awarded for correct method even if the final answer is wrong. Use proper mathematical language and notation. These questions prepare you for Class 10 board exams where coordinate geometry carries significant weight.

Q22. Three vertices of a rectangle are A(2, 1), B(2, 4), and C(6, 4). Find the coordinates of the fourth vertex D and plot all four points on a Cartesian plane. Verify that opposite sides are parallel to the axes. (5 marks)
Q23. A point P lies on the x-axis and is equidistant from the points A(2, 3) and B(4, 1). Without using the distance formula, explain how you would find the x-coordinate of P. (3 marks)
Q24. If the coordinates of a point are (a, b) where a and b are natural numbers less than 5, list all possible points in Quadrant I. How many such points are there? (3 marks)

Case Study Question (4 marks)

Case-study questions are a recent addition to CBSE exam patterns, designed to test your ability to extract information from real-world contexts and apply coordinate geometry concepts. A short paragraph describes a situation involving coordinates—such as a city map, a treasure hunt, or GPS locations—followed by 3-4 sub-questions. These questions assess reading comprehension, data interpretation, and mathematical application simultaneously. In Class 9 Mathematics Chapter 3, case studies often involve plotting locations, identifying quadrants, or reasoning about distances and directions on a plane. Read the passage carefully and underline key numerical data and coordinate pairs. Answer each sub-question independently; they usually build on the same scenario but test different skills. Case-based questions carry 4 marks in total, making them high-value items worth careful attention during practice and exams.

Answer Key with Explanations

The answer key provides correct answers and step-by-step explanations for every question in this worksheet. Detailed solutions help you understand not just what the answer is, but why it is correct and how to arrive at it systematically. Use the answer key for self-assessment after attempting the worksheet on your own. Mark each answer and note questions where you made errors or guessed. Review the explanations for those questions carefully and rework them without looking at the solution. This active learning approach builds deeper understanding and prevents repeated mistakes. For CBSE Class 9 Mathematics Chapter 3, common errors include confusing abscissa with ordinate, incorrect sign conventions, and misidentifying quadrants. The explanations highlight these pitfalls and reinforce correct reasoning. Keep this answer key handy during revision and refer to it whenever you practice similar questions from NCERT or other sources.

A1. (B) II — x = −5 is negative, y = 2 is positive, so Quadrant II.
A2. (A) 0 — Any point on the y-axis has x-coordinate (abscissa) equal to 0.
A3. (C) (−, −) — In Quadrant III, both coordinates are negative.
A4. (D) (0, 0) — The origin is the intersection of the axes.
A5. (B) y-axis — x-coordinate is 0, so the point lies on the y-axis.
A6. (B) (4, −3) — Reflection in the x-axis changes the sign of the y-coordinate.
A7. x-axis
A8. ordinate
A9. origin
A10. positive; negative
A11. abscissa
A12. True — y = 0 means the point is on the x-axis.
A13. False — In Quadrant II, x is negative but y is positive.
A14. True — Every point on the x-axis has y-coordinate 0.
A15. True — Both x and y are negative in Quadrant III.
A16. False — Reflection in the y-axis changes the sign of the x-coordinate, giving (−a, b).
A17. Plot: A(2, 3) in Quadrant I, B(−1, 4) in Quadrant II, C(−3, −2) in Quadrant III. Draw axes, mark origin, plot each point by moving x units horizontally and y units vertically.
A18. Any points of the form (0, y), e.g., (0, 5) and (0, −3). The x-coordinate must be 0.
A19. The point (−4, 0) lies on the negative x-axis because y-coordinate is 0.
A20. Reflection in the x-axis changes the sign of y, so (3, −5) becomes (3, 5).
A21. In Quadrant II, x is negative and y is positive. Equidistant from both axes means |x| = |y| = 6. So coordinates are (−6, 6).
A22. Fourth vertex D = (6, 1). Plot A(2,1), B(2,4), C(6,4), D(6,1). AB is vertical (x = 2), CD is vertical (x = 6). BC is horizontal (y = 4), AD is horizontal (y = 1). Opposite sides are parallel to axes, confirming a rectangle.
A23. Since P is on the x-axis, its coordinates are (x, 0). For P to be equidistant from A and B, the perpendicular from P to the line AB would bisect AB. By symmetry or reasoning, x-coordinate of P is the average of x-coordinates of A and B if they are symmetric about a vertical line, but without distance formula, one can use graphical symmetry or midpoint logic. (Detailed coordinate calculation would use distance formula, which is Class 10 content, so reasoning is encouraged.)
A24. Natural numbers less than 5 are 1, 2, 3, 4. Quadrant I requires both coordinates positive. Possible points: (1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4). Total = 4 × 4 = 16 points.
Case Study Answers: (i) Cafeteria C(−3, −4) is in Quadrant III (both coordinates negative). (ii) Fountain F(3, 4) is in Quadrant I; Jogging track J(4, −3) is in Quadrant IV. (iii) From origin (0, 0) to F(3, 4), move 3 units right (positive x-direction) and 4 units up (positive y-direction). Total displacement is 3 units east and 4 units north in coordinate terms.

How to Use This Worksheet Effectively for CBSE Exam Preparation

This worksheet is designed as a complete practice tool for CBSE Class 9 Mathematics Chapter 3 Coordinate Geometry. To get maximum benefit, print it out and attempt all sections in one 90-minute sitting, simulating exam conditions. Keep your NCERT textbook closed during the attempt. Use a pencil, eraser, ruler, and graph paper if needed for plotting. After completing, check your answers against the detailed answer key and calculate your score. Identify question types where you lost marks—whether MCQs, fill-in-blanks, or long answers—and revisit those concepts in your NCERT textbook or Class 9 Mathematics notes. Reattempt incorrect questions after a day or two to ensure the concepts have solidified. This active recall method is proven to enhance retention and exam performance. For students aiming for 90+ scores in CBSE Mathematics, mastering Coordinate Geometry worksheets like this one is non-negotiable because coordinate concepts form the foundation for Class 10 board topics like distance and section formulas.

Attempt the worksheet in one 90-minute session without breaks to build stamina.
Use graph paper or draw neat Cartesian planes with labeled axes for plotting questions.
Self-check with the answer key immediately after finishing to identify weak areas.
Rework all incorrect or guessed questions within 48 hours for better retention.
Track your score over multiple worksheets to measure improvement over time.

Common Mistakes Students Make in Coordinate Geometry and How to Avoid Them

Even strong students make avoidable errors in CBSE Class 9 Mathematics Chapter 3 Coordinate Geometry. One frequent mistake is reversing the order of coordinates, writing (y, x) instead of (x, y). Always remember: abscissa (x) comes first, ordinate (y) second. Another common error is misidentifying quadrants due to incorrect sign interpretation. Make a small quadrant chart in your rough work before answering such questions. Students also forget that points on the axes do not belong to any quadrant; for example, (0, 5) is on the y-axis, not in Quadrant I or II. When plotting points, many students skip labeling the axes or marking the origin, leading to mark deductions even if the plot is correct. In reflection questions, students often flip the wrong coordinate; remember that reflection in the x-axis changes the y-coordinate, and reflection in the y-axis changes the x-coordinate. Finally, in case-study questions, students sometimes answer based on assumptions rather than the given data. Underline key facts in the passage and refer back to them for each sub-question. Practicing with worksheets like this one and carefully reviewing the answer key helps eliminate these errors over time.

Always write coordinates in (x, y) order; x is horizontal, y is vertical.
Draw a quick quadrant sign chart: I(+,+), II(−,+), III(−,−), IV(+,−) before answering.
Points on axes have one coordinate as 0 and belong to no quadrant.
Label your axes, origin, and plotted points clearly to secure full marks in diagrams.
Reflection in x-axis: flip y; reflection in y-axis: flip x. Write this rule in your notebook.
In case studies, extract numbers and coordinates carefully; do not assume or infer beyond the text.

Boost Your Coordinate Geometry Skills with CBSETUTOR.ai

If you find any question in this worksheet challenging or want instant help with a similar problem, CBSETUTOR.ai is your 24×7 AI tutor. Students from Class 6 to Class 12 can upload a photo of any Mathematics problem—be it from NCERT, sample papers, or worksheets like this one—and receive step-by-step solutions within seconds. The platform covers the entire CBSE syllabus, including Coordinate Geometry, with clear explanations in Indian English that match how teachers explain concepts in school. At just ₹999 per month for all classes (6-12), it is more affordable than a single private tuition session and offers unlimited doubt solving. Parents across metros like Delhi, Bengaluru, and Mumbai, and in Tier-2 cities where quality coaching is scarce, trust CBSETUTOR.ai to give their children the academic support they need. Start with a free 3-day trial—no credit card required—and see how instant, personalized feedback transforms your child's confidence and performance in Mathematics. Whether it is mastering Coordinate Geometry or any other chapter, CBSETUTOR.ai ensures no student is left behind.

Upload any Class 9 Mathematics question via photo and get instant, step-by-step solutions.
Unlimited doubt-solving across all CBSE subjects and classes at a flat ₹999/month.
3-day free trial with no credit card needed; cancel anytime if not satisfied.
Covers NCERT, sample papers, previous year questions, and worksheet problems.
Available 24×7, perfect for last-minute exam prep or after-school revision.

Frequently asked questions

What topics are covered in CBSE Class 9 Mathematics Chapter 3 Coordinate Geometry?+

Chapter 3 introduces the Cartesian plane, x-axis, y-axis, origin, and quadrants. Students learn to plot points using ordered pairs (x, y), understand abscissa and ordinate, identify quadrants based on coordinate signs, and work with reflections. NCERT exercises focus on plotting, quadrant identification, and basic applications. Distance and section formulas are introduced in Class 10.

How much time should I spend on this worksheet?+

This worksheet is designed for a 90-minute session. Allocate 10-15 minutes for Sections A, B, and C combined, 20 minutes for Section D short answers, 30 minutes for Section E long answers, 10 minutes for the case study, and 15 minutes for review. Adjust based on your speed, but aim to complete it in one sitting to build exam stamina.

What is the difference between abscissa and ordinate?+

Abscissa is the x-coordinate of a point, representing its horizontal distance from the y-axis. Ordinate is the y-coordinate, representing vertical distance from the x-axis. In the ordered pair (x, y), x is the abscissa and y is the ordinate. They are always written in that order. Mixing them up is a common error in exams.

Do points on the axes belong to any quadrant?+

No. Points on the x-axis have y-coordinate 0, and points on the y-axis have x-coordinate 0. They lie on the boundaries between quadrants and do not belong to any specific quadrant. For example, (5, 0) is on the x-axis, and (0, −3) is on the y-axis. This is a frequent MCQ trap in CBSE exams.

How are reflections in the x-axis and y-axis different?+

Reflection in the x-axis flips a point vertically, changing the sign of the y-coordinate. So (a, b) becomes (a, −b). Reflection in the y-axis flips a point horizontally, changing the sign of the x-coordinate, giving (−a, b). Remember: x-axis reflection affects y, y-axis reflection affects x. This is tested in short-answer and MCQ formats.

Why is Coordinate Geometry important for Class 10 boards?+

Coordinate Geometry in Class 9 lays the foundation for major Class 10 board topics: distance formula, section formula, midpoint, area of triangles, and collinearity. The 2025 CBSE Class 10 board paper carries 6 marks for Coordinate Geometry. Mastering Chapter 3 now makes those questions straightforward later and saves time during board preparation.

Can I practice this worksheet multiple times?+

Absolutely. After your first attempt, review the answer key, understand all mistakes, and reattempt incorrect questions. Wait a week and try the entire worksheet again to test retention. You can also modify numbers in questions for fresh practice. Repeated practice builds speed and accuracy, both crucial for scoring well in CBSE term exams.

What should I do if I score low on Section E HOTS questions?+

HOTS questions require multi-step reasoning and conceptual clarity. Revisit NCERT examples and miscellaneous exercises. Practice similar problems from NCERT Exemplar or previous year papers. Draw diagrams for every problem. Discuss challenging questions with your teacher or use CBSETUTOR.ai to get instant, step-by-step solutions. Regular practice of HOTS problems improves logical thinking and exam confidence.

How are case-study questions structured in CBSE exams?+

Case-study questions present a real-world scenario (e.g., a map, GPS data, or park layout) followed by 3-4 sub-questions worth 1-2 marks each. They assess reading comprehension, data extraction, and application of coordinate concepts. In Class 9 Chapter 3, case studies involve plotting points, identifying quadrants, or reasoning about positions. They carry 4 marks and are scoring if you read carefully.

Where can I find more worksheets and practice material for Class 9 Mathematics?+

NCERT textbooks and exemplar books are primary resources. CBSE official sample papers and previous year question papers are available on cbse.nic.in. For unlimited doubt-solving and personalized practice, try CBSETUTOR.ai, which offers step-by-step solutions to any problem via photo upload. The platform covers all chapters and question types for Classes 6-12 at ₹999/month with a 3-day free trial.

Related resources

Ready to give your Class 9 child the tutor that never sleeps?

CBSETUTOR.ai covers every chapter in the Class 9 NCERT syllabus — Maths, Science, Social Science, English, Hindi and more. 24×7. Patient. Unlimited. 3-day free trial.

Start your child's 3-day free trial →