Orienting Yourself: The Use of Coordinates – Class 9 Notes
🧭 1. Meaning of Orientation
Orientation means identifying or describing the position of a point or object in a plane using a fixed reference system.
In mathematics, we use a coordinate system for accurate positioning.
📍 2. Cartesian Coordinate System
The coordinate system consists of two perpendicular number lines:
- x-axis (horizontal line) → represents left-right movement
- y-axis (vertical line) → represents up-down movement
👉 Their intersection point is called the Origin (O)
Coordinates of origin = (0, 0)
📐 3. Coordinates of a Point
A point in a plane is represented as:
👉 (x, y)
- x-coordinate (abscissa) → distance from y-axis
- y-coordinate (ordinate) → distance from x-axis
📌 Order matters: x first, then y
🔲 4. Quadrants of the Cartesian Plane
The axes divide the plane into four regions called quadrants:
| Quadrant | Signs of (x, y) |
|---|---|
| I | (+, +) |
| II | (−, +) |
| III | (−, −) |
| IV | (+, −) |
👉 Points lying on axes do not belong to any quadrant.
📊 5. Plotting a Point
Steps to plot (x, y):
- Start from origin
- Move along x-axis:
- right if x is positive
- left if x is negative
- Move parallel to y-axis:
- up if y is positive
- down if y is negative
- Mark the point
📍 6. Points on Axes
- On x-axis → y = 0 → (x, 0)
- On y-axis → x = 0 → (0, y)
👉 Origin is the only point common to both axes.
🔁 7. Reflection of Points
Reflection means mirror image across an axis.
- Reflection in x-axis → (x, −y)
- Reflection in y-axis → (−x, y)
- Reflection in origin → (−x, −y)
🧠 8. Important Observations
- Sign of coordinates determines location in quadrant
- Distance from axes helps in plotting
- Order of coordinates cannot be changed
- Points on axes have one coordinate zero
🌍 9. Real-Life Applications
Coordinate system is used in:
- GPS navigation systems
- Maps and city planning
- Computer graphics and animation
- Robotics and gaming
- Data representation in graphs
📝 10. Key Points to Remember
Reflection changes sign depending on axis
Coordinates are written as (x, y)
Origin = (0, 0)
Four quadrants exist
Axes are perpendicular
Coordinates – 50 Tough Questions with Answers (Class 9)
🔢 Section A: Conceptual (1–10)
1. What are the coordinates of origin?
👉 (0, 0)
2. How many quadrants are there in a Cartesian plane?
👉 4
3. What are the signs in Quadrant II?
👉 (−, +)
4. A point lies on x-axis. What is its y-coordinate?
👉 0
5. A point lies on y-axis. What is its x-coordinate?
👉 0
6. Which axis is horizontal?
👉 x-axis
7. Which axis is vertical?
👉 y-axis
8. Can a point lie in two quadrants?
👉 No
9. What is abscissa?
👉 x-coordinate
10. What is ordinate?
👉 y-coordinate
📍 Section B: Identifying Quadrants (11–20)
11. (3, 5) lies in which quadrant?
👉 I
12. (−4, 6) lies in which quadrant?
👉 II
13. (−7, −2) lies in which quadrant?
👉 III
14. (8, −9) lies in which quadrant?
👉 IV
15. (−1, 0) lies on which axis?
👉 x-axis
16. (0, −5) lies on which axis?
👉 y-axis
17. (0, 0) is called?
👉 Origin
18. Which quadrant has all positive coordinates?
👉 I
19. Which quadrant has all negative coordinates?
👉 III
20. A point (x, y) is in Quadrant IV. Signs?
👉 (+, −)
🔁 Section C: Reflection (21–30)
21. Reflection of (3, 4) in x-axis
👉 (3, −4)
22. Reflection of (−2, 5) in x-axis
👉 (−2, −5)
23. Reflection of (4, −3) in y-axis
👉 (−4, −3)
24. Reflection of (−6, −7) in y-axis
👉 (6, −7)
25. Reflection of (5, 0) in x-axis
👉 (5, 0)
26. Reflection of (0, 8) in y-axis
👉 (0, 8)
27. Reflection of (−3, −4) in origin
👉 (3, 4)
28. Reflection of (7, −2) in origin
👉 (−7, 2)
29. If a point lies on x-axis, reflection in x-axis is?
👉 Same point
30. If a point lies on y-axis, reflection in y-axis is?
👉 Same point
📊 Section D: Analytical Thinking (31–40)
31. Distance from y-axis of (5, 3)
👉 5 units
32. Distance from x-axis of (−4, 6)
👉 6 units
33. Which coordinate determines left-right position?
👉 x-coordinate
34. Which coordinate determines up-down position?
👉 y-coordinate
35. Point (−3, 7): move how from origin?
👉 3 left, 7 up
36. Point (6, −2): move how?
👉 6 right, 2 down
37. If x = 0, point lies on?
👉 y-axis
38. If y = 0, point lies on?
👉 x-axis
39. Can (0, 5) be in a quadrant?
👉 No
40. Can (−4, 0) be in a quadrant?
👉 No
🧠 Section E: Higher Order / Application (41–50)
41. Find quadrant of (−8, 9)
👉 II
42. Find quadrant of (12, −5)
👉 IV
43. Find quadrant of (−10, −1)
👉 III
44. Find quadrant of (7, 11)
👉 I
45. Write reflection of (−5, 6) in y-axis
👉 (5, 6)
46. Write reflection of (2, −8) in x-axis
👉 (2, 8)
47. Reflection of (−3, −9) in origin
👉 (3, 9)
48. Which point lies on both axes?
👉 (0, 0)
49. A point has x = 0 and y = 0. Name it.
👉 Origin
50. What happens to coordinates after reflection in origin?
👉 Signs of both x and y change