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MathematicsClass 9Orienting Yourself: The Use of Coordinates

Orienting Yourself: The Use of Coordinates | Class 9 Mathematics Notes

By ConceptScroll Team · Published on 17 July 2026 · 5 min read

Orienting Yourself: The Use of Coordinates – this guide gives you a concise, exam-ready overview of Orienting Yourself: The Use of Coordinates from Class 9 Mathematics, written by ConceptScroll editors and reviewed against the latest NCERT textbook.

1.3 THE 2-D CARTESIAN COORDINATE SYSTEM

This section formally introduces the two-dimensional Cartesian coordinate system, building upon the one-dimensional number line studied in earlier grades. The system consists of two perpendicular lines intersecting at a point called the origin (O), with one line horizontal (x-axis) and the other vertical (y-axis). These axes divide the plane into four quadrants.

Each point in this plane is identified by an ordered pair of numbers (x, y), called coordinates. The x-coordinate represents the horizontal distance from the y-axis, while the y-coordinate represents the vertical distance from the x-axis. Distances to the right of the origin or upwards are positive, while those to the left or downwards are negative.

Points lying on the x-axis have coordinates of the form (x, 0), and points on the y-axis have coordinates (0, y). The origin itself has coordinates (0, 0). The axes and the plane they define are known as the coordinate axes and the Cartesian plane or xy-plane, respectively.

The four quadrants are numbered I to IV, starting from the upper right and moving counterclockwise. Quadrant I contains points with both coordinates positive; Quadrant II has negative x and positive y; Quadrant III has both coordinates negative; Quadrant IV has positive x and negative y.

Examples are given to illustrate points in different quadrants, such as point B at (4.5, 0) on the x-axis, point G at (0, -4.5) on the y-axis, and points S (3, -5) and Q (-5, 3) in Quadrants IV and II respectively. The notation P(x, y) is commonly used to denote the coordinates of a point.

Students are encouraged to explore the properties of points on axes and in quadrants, and to understand the significance of positive and negative coordinates in locating points precisely on the plane.

📊 Diagram: Figure 1.2 shows the coordinate plane with x-axis horizontal and y-axis vertical intersecting at origin O. Points B (4.5, 0), G (0, -4.5), and H (0, 4) are marked on the axes. Figure 1.4 illustrates the four quadrants with points S (3, -5) in Quadrant IV and Q (-5, 3) in Quadrant II.

🧪 Activity: Students are asked to copy Fig. 1.4, mark points S and Q, and also mark points in Quadrants I and III with their coordinates.

🔗 Connection: Leads to Exercise Set 1.1 and 1.2, where students practice plotting points and understanding coordinates in real contexts.

Frequently asked questions

Referring to Fig. 1.3, answer the following questions: (i) If \( \mathrm{D}_1\mathrm{R}_1 \) represents the door to Reiaan's room, how far is the door from the left wall (the y-axis) of the room? How far is the door from the x-axis? (ii) What are the coordinates of \( \mathbf{D}_1 \) ? (iii) If \( \mathbf{R}_1 \) is the point (11.5, 0), how wide is the door? Do you think this is a comfortable width for the room door? If a person in a wheelchair wants to enter the room, will he/she be able to do so easily? (iv) If \( \mathrm{B}_1(0, 1.5) \) and \( \mathrm{B}_2(0, 4) \) represent the ends of the bathroom door, is the bathroom door narrower or wider than the room door?

Solution:

(i) The door \( \mathrm{D}_1\mathrm{R}_1 \) is represented in Fig. 1.3. The distance from the left wall (y-axis) is the x-coordinate of the door points. Since \( \mathbf{D}_1 \) lies at some x-coordinate, the distance from the y-axis is that x-coordinate. Similarly, the distance from the x-axis is the y-coordinate of the door points.

(ii) The coordinates of \( \mathbf{D}_1 \) can be read from the figure. For example, if \( \mathbf{D}_1 \) lies at (11.5, 1.5), then the coordinates are

Think and Reflect 1. What are the standard widths for a room door? Look around your home and in school. 2. Are the doors in your school suitable for people in wheelchairs?

Answers will vary depending on observations:

1. Standard widths for room doors typically range from 0.75 meters to 1.0 meter. Wider doors (around 1.2 to 1.5 meters) are more comfortable and accessible.

2. Doors in schools may or may not be suitable for wheelchair users. Suitable doors should be at least 0.9 meters wide and have ramps or no steps. Students should observe and comment based on their school infrastructure.

Copy Fig. 1.4 and mark S and Q in your diagram. Mark any point P in Quadrant I and any point R in Quadrant III, and write down their coordinates.

Solution:

  • Point S is given as (3, -5), which lies in Quadrant IV.
  • Point Q is (-5, 3), which lies in Quadrant II.
  • Mark these points on a copy of Fig. 1.4.
  • Choose any point P in Quadrant I, for example (2, 3), where both coordinates are positive.
  • Choose any point R in Quadrant III, for example (-4, -2), where both coordinates are negative.
  • Write down the coordinates as above.
Think and Reflect 1. What is the x-coordinate of a point on the y-axis? 2. Is there a similar generalisation for a point on the x-axis? 3. Does point Q (y, x) ever coincide with point P (x, y)? Justify your answer. 4. If $x \neq y$, then $(x, y) \neq (y, x)$; and $(x, y) = (y, x)$ if and only if $x = y$. Is this claim true?

Answers:

1. The x-coordinate of a point on the y-axis is always 0 because the point lies on the vertical axis.

2. Similarly, the y-coordinate of a point on the x-axis is always 0.

3. Point Q (y, x) coincides with point P (x, y) only if x = y. Otherwise, they are different points.

4. The claim is true. If x ≠ y, then (x, y) ≠ (y, x). If (x, y) = (y, x), then x must equal y.

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