📚 Chapter at a Glance
📖 Introduction to Coordinates
Imagine you are inside a large shopping mall and want to tell your friend exactly where you are standing. Saying “I am somewhere on the second floor” may not be enough.
We need a system that tells us the exact position of an object or point.
Coordinates provide such a system.
The idea of coordinates is used in maps, navigation, computer graphics, games, architecture, science, engineering and many other areas.
🌍 Coordinates in Everyday Life
Coordinates are not only a mathematical idea. We use similar ideas in everyday situations.
- 📍 Finding a location on a map
- 🗺️ Using GPS navigation
- 🎮 Locating a character in a video game
- 💻 Positioning objects on a computer screen
- 🏗️ Planning buildings and structures
- ✈️ Describing positions in aviation
- 🚢 Navigation of ships
📐 The Coordinate Plane
A coordinate plane is a two-dimensional system used to locate points.
It is formed by two perpendicular number lines:
- x-axis – horizontal axis
- y-axis – vertical axis
The point where the two axes intersect is called the origin.
↔️ The X-Axis
The horizontal line in the coordinate plane is called the x-axis.
Values increase as we move towards the right and decrease as we move towards the left.
| Direction | Effect on x-coordinate |
|---|---|
| Right | Positive |
| Left | Negative |
↕️ The Y-Axis
The vertical line in the coordinate plane is called the y-axis.
Values increase as we move upward and decrease as we move downward.
| Direction | Effect on y-coordinate |
|---|---|
| Up | Positive |
| Down | Negative |
⭕ Origin
The point where the x-axis and y-axis intersect is called the origin.
The origin is the reference point from which the coordinates of other points are measured.
🔢 Ordered Pair
The position of a point is represented using an ordered pair.
The first number represents the position along the x-axis.
The second number represents the position along the y-axis.
Second coordinate → y-coordinate
✏️ Solved Examples
A point is located 4 units to the right of the origin and 3 units upward. What are its coordinates?
Moving right gives: x = 4
Moving upward gives: y = 3
A point is 5 units to the left of the origin and 2 units upward.
Left → x = -5
Up → y = 2
A point is 3 units to the right and 4 units downward.
Right → x = 3
Down → y = -4
Consider the point (7, 0).
Since its y-coordinate is zero, the point lies on the x-axis.
Consider the point (0, -6).
Since its x-coordinate is zero, the point lies on the y-axis.
🧭 The Four Quadrants
The x-axis and y-axis divide the coordinate plane into four regions. These regions are called quadrants.
| Quadrant | x-coordinate | y-coordinate |
|---|---|---|
| I | Positive | Positive |
| II | Negative | Positive |
| III | Negative | Negative |
| IV | Positive | Negative |
I → (+,+)
II → (-,+)
III → (-,-)
IV → (+,-)
📍 Identifying the Quadrant
Both coordinates are positive.
x is negative and y is positive.
Both coordinates are negative.
x is positive and y is negative.
📌 How to Plot a Point
To plot a point such as (4, 3):
- Start from the origin (0,0).
- Look at the x-coordinate.
- Move horizontally according to the x-coordinate.
- Then move vertically according to the y-coordinate.
- Mark the final position.
- Label the point.
⚠️ Common Mistakes Students Make
- Writing (y, x) instead of (x, y).
- Forgetting the negative sign.
- Confusing the x-axis with the y-axis.
- Reading the scale incorrectly.
- Forgetting that points on the x-axis have y = 0.
- Forgetting that points on the y-axis have x = 0.
- Identifying quadrants without checking the signs.
📊 Quick Comparison
| Concept | Meaning |
|---|---|
| x-axis | Horizontal axis |
| y-axis | Vertical axis |
| Origin | Point (0,0) |
| x-coordinate | First number in (x,y) |
| y-coordinate | Second number in (x,y) |
| Quadrant | One of the four regions of the coordinate plane |
| Ordered Pair | Representation of a point as (x,y) |
🧠 Competency-Based Questions
A treasure map uses a coordinate system. The treasure is located 6 units east and 4 units north of the starting point.
Question: What coordinates represent the treasure?
Answer: (6, 4)
A point has coordinates (-7, 3).
Question: In which quadrant does the point lie?
Answer: Quadrant II because x is negative and y is positive.
A point is represented by (0, 8).
Question: Where does the point lie?
Answer: On the y-axis because its x-coordinate is zero.
🎯 Class 9 Maths Chapter 1 MCQs
Answer: B. x-axis
Answer: B. y-axis
Answer: C. (0,0)
Answer: B. x-coordinate
Answer: C. (7,0)
Answer: B. (0,5)
Answer: A. I
Answer: B. II
Answer: C. III
Answer: D. IV
Answer: B. (-,+)
Answer: D. (+,-)
Answer: A. x-axis
Answer: B. y-axis
Answer: C. (3,2)
Answer: C. Coordinates are written as (x,y).
Answer: C. (-5,-4)
Answer: B. y-axis
Answer: A. x-axis
Answer: D. All of the above
📝 Class 9 Maths Chapter 1 Worksheet
Section A – Fill in the Blanks
1. The horizontal axis is called the __________.
2. The vertical axis is called the __________.
3. The point where the two axes meet is called the __________.
4. The coordinates of the origin are __________.
5. An ordered pair is written in the form __________.
Section B – True or False
6. The x-axis is vertical.
7. The y-coordinate is written second.
8. The point (5,0) lies on the x-axis.
9. The point (0,5) lies on the x-axis.
10. The coordinates in Quadrant III are both negative.
Section C – Identify the Quadrant
11. (4,7)
12. (-5,3)
13. (-6,-2)
14. (8,-4)
Section D – Identify the Axis
15. (9,0)
16. (0,-7)
17. (-12,0)
18. (0,10)
Section E – Short Answer Questions
19. What are coordinates?
20. What is an ordered pair?
21. What is the origin?
22. What is a coordinate plane?
Section F – Plotting Practice
23. Plot the following points on a coordinate plane:
- A (2,3)
- B (-3,4)
- C (-4,-2)
- D (5,-3)
- E (0,5)
- F (-6,0)
Draw the coordinate plane in your notebook and label all points clearly.
Section G – Competency-Based Questions
24. A game character is located at (-4,5). Which quadrant contains the character?
25. A location is represented by (6,-3). Explain what the signs of its coordinates tell you.
Section H – Higher Order Thinking
26. Two points are A(4,3) and B(3,4). Are they the same point? Explain why.
27. Can a point belong to two different quadrants? Give a reason for your answer.
Section I – Challenge Question
28. A point is 7 units left of the origin and 5 units down. Write its coordinates and identify its quadrant.
✅ Worksheet Answer Key
- x-axis
- y-axis
- Origin
- (0,0)
- (x,y)
- False
- True
- True
- False
- True
- Quadrant I
- Quadrant II
- Quadrant III
- Quadrant IV
- x-axis
- y-axis
- x-axis
- y-axis
- Coordinates are numbers used to locate a point.
- An ordered pair is written as (x,y).
- The origin is the point (0,0).
- A coordinate plane is formed by two perpendicular number lines, the x-axis and y-axis.
- See plotted coordinate plane.
- Quadrant II
- x is positive and y is negative, so the point is in Quadrant IV.
- No. The order of coordinates matters.
- A point on an axis is not considered to be inside a quadrant.
- (-7,-5), Quadrant III
⚡ Quick Revision
1
Coordinates
x-axis
y-axis
(0,0)
(x,y)
(+,+)
(-,+)
(-,-)
(+,-)
🎯 Exam Tips for Chapter 1
- Always remember that coordinates are written as (x,y).
- The first number tells you the horizontal movement.
- The second number tells you the vertical movement.
- A point with y = 0 lies on the x-axis.
- A point with x = 0 lies on the y-axis.
- The origin is always (0,0).
- Use the signs of x and y to identify the quadrant.
- Do not interchange coordinates. For example, (2,5) and (5,2) represent different points.
- When plotting points, carefully check the scale on both axes.
❓ Frequently Asked Questions
What is Chapter 1 of Class 9 Maths?
The chapter is titled Orienting Yourself: The Use of Coordinates.
What are coordinates?
Coordinates are numbers used to specify the position of a point in a coordinate system.
What is the coordinate of the origin?
The origin has coordinates (0,0).
What is an ordered pair?
An ordered pair is a pair of numbers written as (x,y) that specifies the position of a point.
What are the four quadrants?
The four regions formed by the x-axis and y-axis are called Quadrants I, II, III and IV.
Which coordinate comes first?
The x-coordinate comes first and the y-coordinate comes second.
How can I identify the quadrant of a point?
Look at the signs of its x- and y-coordinates. (+,+) is Quadrant I, (-,+) is Quadrant II, (-,-) is Quadrant III and (+,-) is Quadrant IV.
Where does a point with x = 0 lie?
A point whose x-coordinate is zero lies on the y-axis.
Where does a point with y = 0 lie?
A point whose y-coordinate is zero lies on the x-axis.
📚 Class 9 Maths Chapter 1 Study Resources
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