Coordinate Geometry – Easy Notes

 

📘 Chapter 1: Coordinate Geometry – Easy Notes

🌟 1. Introduction

• A coordinate system helps us locate the exact position of a point using numbers.
• Example: Like finding a location on a map using grid lines.
• It connects Geometry + Algebra.

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🧭 2. Cartesian Coordinate System (2-D)

• Made up of two perpendicular lines:
  • ➡️ x-axis (horizontal)
  • ⬆️ y-axis (vertical)
• Their intersection point is called Origin (O)
  👉 Coordinates: (0, 0)

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📍 3. Coordinates of a Point

• A point is written as (x, y)
  • x-coordinate → distance from y-axis
  • y-coordinate → distance from x-axis

👉 Example:

• (3, 4) → 3 units right, 4 units up
• (–2, 5) → 2 units left, 5 units up
  

📏 4. Signs of Coordinates

Direction	Sign
Right	+x
Left	–x
Up	+y
Down	–y

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🔲 5. Quadrants

The plane is divided into 4 parts:

Quadrant	Signs
I	(+, +)
II	(–, +)
III	(–, –)
IV	(+, –)

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📌 6. Points on Axes

• On x-axis → (x, 0)
• On y-axis → (0, y)

👉 Important:

• x-coordinate of any point on y-axis = 0
• y-coordinate of any point on x-axis = 0

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🔁 7. Interchanging Coordinates

• (x, y) ≠ (y, x) generally
• They are equal only if x = y

👉 Example:

• (2, 3) ≠ (3, 2)
• (5, 5) = (5, 5)

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📐 8. Distance Between Two Points

For two points:

• A(x₁, y₁)
• B(x₂, y₂)

Distance is:

👉 Based on Pythagoras Theorem

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📊 Special Cases of Distance

• Same y-coordinate:
  👉 Distance = |x₂ – x₁|
• Same x-coordinate:
  👉 Distance = |y₂ – y₁|

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🧠 9. Key Concepts to Remember

• Origin = (0, 0)
• Coordinates always written as (x, y)
• First value → horizontal movement
• Second value → vertical movement
• Quadrants depend on signs
• Distance formula helps find length between points

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🎯 10. Quick Examples

1. Point (0, 5) lies on → y-axis
2. Point (–3, 0) lies on → x-axis
3. Point (4, –2) lies in → Quadrant IV

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💡 11. Think & Reflect Answers

1. x-coordinate on y-axis = 0
2. y-coordinate on x-axis = 0
3. (x, y) = (y, x) only when x = y
4. Statement is True

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✨ 12. Real-Life Application

• Maps & navigation 📍
• GPS systems 🛰️
• Game design 🎮
• Architecture 🏗️

📝 Section A: MCQs (Objective Questions)

Choose the correct answer:

1. The point of intersection of x-axis and y-axis is called:
   • (a) Quadrant
   • (b) Origin
   • (c) Axis
   • (d) Plane
2. The coordinates of the origin are:
   • (a) (1, 0)
   • (b) (0, 1)
   • (c) (0, 0)
   • (d) (1, 1)
3. A point on the x-axis has:
   • (a) x = 0
   • (b) y = 0
   • (c) x = y
   • (d) none
4. A point (–3, 4) lies in:
   • (a) Quadrant I
   • (b) Quadrant II
   • (c) Quadrant III
   • (d) Quadrant IV
5. A point (5, –2) lies in:
   • (a) Quadrant I
   • (b) Quadrant II
   • (c) Quadrant III
   • (d) Quadrant IV
6. The x-coordinate of a point on y-axis is:
   • (a) 1
   • (b) –1
   • (c) 0
   • (d) any number
7. The y-coordinate of a point on x-axis is:
   • (a) 0
   • (b) 1
   • (c) –1
   • (d) any number
8. The point (0, –5) lies on:
   • (a) x-axis
   • (b) y-axis
   • (c) origin
   • (d) quadrant III
9. Which of the following lies in Quadrant III?
   • (a) (–2, –3)
   • (b) (2, –3)
   • (c) (–2, 3)
   • (d) (2, 3)
10. If (x, y) = (y, x), then:

• (a) x ≠ y
• (b) x = y
• (c) x = 0
• (d) y = 0

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Distance Based MCQs

11. Distance between (2, 3) and (2, 7) is:

• (a) 5
• (b) 4
• (c) 3
• (d) 6

12. Distance between (–1, 2) and (3, 2) is:

• (a) 2
• (b) 4
• (c) 6
• (d) 5

13. Distance between (0, 0) and (3, 4) is:

• (a) 7
• (b) 5
• (c) 6
• (d) 4

14. Distance between (1, 1) and (4, 5) is:

$d = \sqrt{(4-1)^2 + (5-1)^2}$

• (a) 3
• (b) 4
• (c) 5
• (d) 6

15. Distance between (–2, –3) and (1, 1) is:

• (a) 5
• (b) 6
• (c) 7
• (d) 4

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📘 Section B: Worksheet (Short Answer)

Q1. Fill in the blanks

1. The origin is ______.
2. A point on y-axis has x-coordinate = ______.
3. Quadrant II has signs ______.
4. Coordinates of a point are written as ______.
5. Distance on x-axis = ______ difference.

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Q2. Answer the following

1. Write coordinates of:
   • A point on x-axis
   • A point on y-axis
2. Identify the quadrant:
   • (–4, 5)
   • (3, –6)
   • (–2, –8)
3. Find distance:
   • (2, 5) and (2, 1)
   • (–3, 4) and (1, 4)

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Q3. Long Answer Questions

1. Plot points A (2, 3), B (–2, 3), C (–2, –3), D (2, –3).
   • What shape is formed?
2. Find distance between points (3, 2) and (7, 5)
3. Verify whether (2, 2) = (2, 2) and (2, 3) = (3, 2)

Worksheet Answers

Fill in the blanks

1. (0, 0)
2. 0
3. (–, +)
4. (x, y)
5. absolute

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Short Answers

• On x-axis → (x, 0)
• On y-axis → (0, y)

Quadrants:

• (–4, 5) → II
• (3, –6) → IV
• (–2, –8) → III

Distances:

• (2,5) & (2,1) → 4
• (–3,4) & (1,4) → 4

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Long Answers

1. Shape → Rectangle
2. Distance:

$d = \sqrt{(7-3)^2 + (5-2)^2} = 5$

• (2,2) = (2,2) ✔️
• (2,3) ≠ (3,2) ❌ 

📝 Class 9 Mathematics Test Paper

Chapter: Coordinate Geometry

Time: 1.5 Hours
Maximum Marks: 40

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🔹 Section A (1 × 10 = 10 marks)

MCQs (Attempt all questions)

1. The coordinates of the origin are:
   (a) (1, 1)
   (b) (0, 0)
   (c) (0, 1)
   (d) (1, 0)
2. A point on the y-axis has:
   (a) x = 0
   (b) y = 0
   (c) x = y
   (d) none
3. The point (–4, –3) lies in:
   (a) I quadrant
   (b) II quadrant
   (c) III quadrant
   (d) IV quadrant
4. Which point lies on x-axis?
   (a) (0, 5)
   (b) (4, 0)
   (c) (2, 2)
   (d) (–3, 3)
5. The point (3, –5) lies in:
   (a) I
   (b) II
   (c) III
   (d) IV
6. If (x, y) = (y, x), then:
   (a) x ≠ y
   (b) x = y
   (c) x = 0
   (d) y = 0
7. Distance between (2, 3) and (2, 7) is:
   (a) 5
   (b) 4
   (c) 3
   (d) 6
8. Distance between (0, 0) and (3, 4) is:
   (a) 7
   (b) 5
   (c) 6
   (d) 4
9. A point (0, –7) lies on:
   (a) x-axis
   (b) y-axis
   (c) origin
   (d) quadrant IV
10. The coordinates of a point in Quadrant II are:
    (a) (+, +)
    (b) (–, +)
    (c) (–, –)
    (d) (+, –)

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🔹 Section B (2 × 5 = 10 marks)

Short Answer Questions

11. Write coordinates of:
    (i) A point on x-axis
    (ii) A point on y-axis
12. Identify the quadrant of:
    (i) (–3, 5)
    (ii) (4, –6)
13. Find distance between (–2, 3) and (4, 3)
14. What are the coordinates of the origin? Explain its importance.
15. Write whether True or False:
    (i) (2, 3) = (3, 2)
    (ii) A point on x-axis has y = 0

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🔹 Section C (4 × 5 = 20 marks)

Long Answer Questions

16. Plot the points A (2, 3), B (–2, 3), C (–2, –3), D (2, –3).
    (i) Name the figure formed
    (ii) Find the length and breadth

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17. Find the distance between points (1, 2) and (5, 5)

$d = \sqrt{(5-1)^2 + (5-2)^2}$

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18. Determine the quadrant of the following points and justify:
    (i) (–5, –4)
    (ii) (6, –2)
    (iii) (–3, 7)
    (iv) (4, 8)

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19. Verify whether (x, y) = (y, x) for:
    (i) (3, 3)
    (ii) (2, 5)

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20. Find the distance between (–3, –4) and (0, 0)

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✅ Answer Key

Section A

1-b, 2-a, 3-c, 4-b, 5-d, 6-b, 7-b, 8-b, 9-b, 10-b

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Section B

11. (x, 0), (0, y)
12. II, IV
13. 6
14. (0, 0), starting point of plane
15. False, True

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Section C

16. Rectangle; Length = 4, Breadth = 6

Distance = 5

(i) III
(ii) IV
(iii) II
(iv) I

(i) Equal
(ii) Not equal

Distance = 5