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I. Chapter Summary

This chapter introduces students to the basics of coordinate geometry, which connects algebra with geometry. It explains how to locate points on a plane using ordered pairs (x, y), introduces the Cartesian coordinate system, and helps students visualize points in different quadrants. The chapter covers plotting points, understanding the coordinate axes, and identifying the quadrant of a point. These concepts lay the groundwork for analytical geometry in higher classes.

II. Key Concepts Covered

Concept	Explanation
Cartesian System	A method of locating a point on a plane using two intersecting perpendicular lines — x-axis and y-axis.
Origin	The point of intersection of x-axis and y-axis; represented by (0, 0).
Axes
→ x-axis: horizontal line
→ y-axis: vertical line
Coordinates	An ordered pair (x, y) that represents the location of a point with respect to the origin.
Quadrants	The coordinate plane is divided into four regions:
→ Quadrant I (+, +)
→ Quadrant II (–, +)
→ Quadrant III (–, –)
→ Quadrant IV (+, –)
Plotting Points	Marking a point on the graph paper by identifying its x and y coordinates.
Signs of Coordinates	Determined by the quadrant in which the point lies.

III. Important Questions

(A) Multiple Choice Questions (1 Mark)

1. What are the coordinates of the origin?
   a) (1, 0)
   b) (0, 1)
   c) (1, 1)
   d) (0, 0) ✔️
2. In which quadrant does the point (–3, 4) lie?
   a) I
   b) II ✔️
   c) III
   d) IV
3. Which of the following is not a valid coordinate pair?
   a) (0, –2)
   b) (–5, 3)
   c) (7, 0)
   d) (x, y) ✔️
4. The x-coordinate of any point on the y-axis is:
   a) 0 ✔️
   b) 1
   c) y
   d) undefined
   (PYQ 2019)

(B) Short Answer Questions (2/3 Marks)

1. Write the coordinates of the point lying on the x-axis at a distance of 5 units from the origin.
2. Plot the points A(2, 3), B(–3, 1), and C(–2, –4) on the graph paper and identify the quadrants they lie in.
3. Identify the quadrant of the point (–1, –3). (PYQ 2018)
4. Write the coordinates of a point that lies in the fourth quadrant and is 2 units below the x-axis and 3 units right of the origin.

(C) Long Answer Questions (5 Marks)

1. Plot the following points on the graph: P(3, 4), Q(–4, 3), R(–2, –5), and S(5, –3). Identify the quadrant of each point and form a quadrilateral.
2. Explain how the sign of x and y helps in determining the quadrant of a point. Illustrate with 4 examples.
3. Describe the Cartesian coordinate system in detail and explain the significance of origin and axes.
4. A point is 3 units right of the y-axis and 4 units below the x-axis. What are its coordinates? Plot the point and two more points that lie in the same quadrant.

(D) HOTS (Higher Order Thinking Skills)

1. Can a point lie in more than one quadrant at a time? Why or why not?
2. If a point lies on both the x-axis and the y-axis, what can you say about its coordinates? Explain with reasoning.

IV. Key Formulas/Concepts

Term/Concept	Definition/Example
Origin	The point (0, 0) where the x-axis and y-axis intersect.
Coordinate of a point on x-axis	(x, 0)
Coordinate of a point on y-axis	(0, y)
Quadrant Identification
→ (+, +): Quadrant I
→ (–, +): Quadrant II
→ (–, –): Quadrant III
→ (+, –): Quadrant IV

V. Deleted Portions (CBSE 2025–2026)

No portions have been deleted from this chapter as per the rationalized NCERT textbooks.

VI. Chapter-Wise Marks Bifurcation (Estimated – CBSE 2025–2026)

Unit/Chapter	Estimated Marks	Type of Questions Typically Asked
Chapter 3: Coordinate Geometry	4–6 Marks	1 MCQ, 1 Short Answer, 1 Long Answer, 1 Graph-Based Question

VII. Previous Year Questions (PYQs)

Mark	Question	Year
1 mark	In which quadrant does (–4, –5) lie?	PYQ 2020
2 marks	Write the coordinates of the point on x-axis at distance 6 units to the left of origin.	PYQ 2019
3 marks	Plot given points and mention their quadrants.	PYQ 2018
5 marks	Graphically locate 4 points and form a figure. Label and identify it.	PYQ 2020

VIII. Real-World Application Examples

• GPS & Navigation: Uses coordinate systems to locate places on Earth.
• Map Reading: Coordinates help identify locations on maps.
• Robotics & Gaming: Object positions and motion paths are based on coordinate geometry.
• Architecture: Design layouts use grid coordinates for accurate planning.

IX. Student Tips & Strategies for Success

 Time Management

• Spend 2 days learning theory and rules
• Spend 2 days on plotting and quadrant questions

 Exam Preparation

• Practice graph plotting with accurate scaling
• Label all axes, points, and quadrants clearly in the graph

 Stress Management

• Use graph paper regularly while practicing
• Play coordinate-based games like Battleship or Desmos activities

X. Career Guidance & Exploration

• Streams After Class 10:
  ➤ Science (Engineering, Robotics, Architecture)
  ➤ Commerce (Geospatial Finance, Analytics)
• Career Paths:
  ➤ Architect
  ➤ Urban Planner
  ➤ Game Designer
  ➤ Surveyor
  ➤ Data Analyst
• Competitive Exams:
  ➤ NTSE
  ➤ SOF IMO
  ➤ RMO
  ➤ CUET (Math Section)

XI. Important Notes

 Always use graph paper in exams for plotting-based questions.
 Label all parts: x-axis, y-axis, origin, quadrants, and plotted points.
 Revise signs of coordinates based on quadrant — common exam confusion.
 Keep practicing mixed questions (plotting + theory) for full preparation.