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Class 9 Maths Chapter 3 Coordinate Geometry – Exercise 3.1 NCERT Solutions

Class 9 Maths Chapter 3 Coordinate Geometry – Exercise 3.1 NCERT Solutions

Introduction

Exercise 3.1 introduces the Cartesian coordinate system. You’ll learn how to represent points using ordered pairs (x,y), plot them on the plane, and understand quadrants.

Key Concept

  • Coordinates: A point is represented as (x,y), where x is the horizontal distance (abscissa) and y is the vertical distance (ordinate).

  • Quadrants:

    • Quadrant I: (+x,+y)

    • Quadrant II: (−x,+y)

    • Quadrant III: (−x,−y)

    • Quadrant IV: (+x,−y)

Solved Questions (Step by Step)

Q1. Plot the point (2,3).

Solution:

  • Move 2 units along x‑axis, 3 units along y‑axis.

  • Point lies in Quadrant I.

Q2. Plot the point (−2,3).

Solution:

  • Move 2 units left along x‑axis, 3 units up along y‑axis.

  • Point lies in Quadrant II.

Q3. Plot the point (−3,−4).

Solution:

  • Move 3 units left, 4 units down.

  • Point lies in Quadrant III.

Q4. Plot the point (4,−2).

Solution:

  • Move 4 units right, 2 units down.

  • Point lies in Quadrant IV.

Q5. Plot the point (0,5).

Solution:

  • Lies on y‑axis, 5 units above origin.

Q6. Plot the point (6,0).

Solution:

  • Lies on x‑axis, 6 units right of origin.

Q7. Plot the point (0,−3).

Solution:

  • Lies on y‑axis, 3 units below origin.

Q8. Plot the point (−5,0).

Solution:

  • Lies on x‑axis, 5 units left of origin.

Q9. Identify quadrant of (7,−8).

Solution:

  • x>0,y<0.

  • Quadrant IV.

Q10. Identify quadrant of (−9,6).

Solution:

  • x<0,y>0.

  • Quadrant II.

Q11. Identify quadrant of (−4,−7).

Solution:

  • x<0,y<0.

  • Quadrant III.

Q12. Identify quadrant of (5,9).

Solution:

  • x>0,y>0.

  • Quadrant I.

Q13. Plot the point (1,−1).

Solution:

  • Lies in Quadrant IV.

Q14. Plot the point (−1,1).

Solution:

  • Lies in Quadrant II.

Q15. Plot the point (−2,−2).

Solution:

  • Lies in Quadrant III.

FAQs (10 for Exercise 3.1)

  1. Q: What is the origin? A: The point (0,0) where x‑axis and y‑axis intersect.

  2. Q: How many quadrants are there? A: Four quadrants in the Cartesian plane.

  3. Q: What does the x‑coordinate represent? A: Horizontal distance from the origin.

  4. Q: What does the y‑coordinate represent? A: Vertical distance from the origin.

  5. Q: What is the sign convention in Quadrant I? A: Both x and y are positive.

  6. Q: What is the sign convention in Quadrant II? A: x is negative, y is positive.

  7. Q: What is the sign convention in Quadrant III? A: Both x and y are negative.

  8. Q: What is the sign convention in Quadrant IV? A: x is positive, y is negative.

  9. Q: Where do points with x = 0 lie? A: On the y‑axis.

  10. Q: Where do points with y = 0 lie? A: On the x‑axis.

Conclusion

Exercise 3.1 has 15 questions that build your foundation in coordinate geometry. You now know how to plot points, identify quadrants, and understand the Cartesian plane.

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