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MathematicsClass 9Orienting Yourself: The Use of

Orienting Yourself: The Use of | Class 9 Mathematics Notes

By ConceptScroll Team · Published on 17 July 2026 · 4 min read

Orienting Yourself: The Use of | Class 9 Mathematics Notes

Orienting Yourself: The Use of – this guide gives you a concise, exam-ready overview of Orienting Yourself: The Use of 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, which uses two perpendicular lines called axes to locate points in a plane. The horizontal line is called the x-axis and the vertical line is called the y-axis. Their intersection point is the origin, denoted by O, with coordinates (0, 0).

Distances from the origin are marked in equal units along both axes. Points to the right of the origin on the x-axis and above the origin on the y-axis are positive; points to the left and below are negative. This allows representation of points in all four quadrants of the plane.

Coordinates of a point are written as (x, y), where x is the distance from the y-axis measured along the x-axis, and y is the distance from the x-axis measured along the y-axis. Points lying on the axes have one coordinate zero, for example, (4.5, 0) lies on the x-axis, and (0, -4.5) lies on the y-axis.

The section also introduces the concept of quadrants, the four parts into which the axes divide the plane. Quadrant I has positive x and y, Quadrant II has negative x and positive y, Quadrant III has negative x and y, and Quadrant IV has positive x and negative y. Understanding these quadrants helps in locating points precisely.

The section ends with an exercise based on a room layout (Fig. 1.3) where students are asked to find coordinates of points and distances, reinforcing the practical use of coordinates.

📊 Diagram: Fig. 1.2: Structure of the coordinate plane; Fig. 1.3: Sketch of Reiaan's room

🧪 Activity: Exercise Set 1.1: Questions based on coordinates of points in Reiaan's room layout.

🔗 Connection: Leads to further exploration of points in quadrants and plotting points not on axes.

Frequently asked questions

Referring to Fig. 1.3, answer the following questions: (i) If D₁R₁ 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 D₁? (iii) If R₁ 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 B₁(0, 1.5) and B₂(0, 4) represent the ends of the bathroom door, is the bathroom door narrower or wider than the room door?

Solution:

(i) The door D₁R₁ is shown in Fig. 1.3. The distance of the door from the left wall (y-axis) is the x-coordinate of the door points. Since D₁ lies on the y-axis (x=0), the door is at 0 units from the y-axis (left wall). The distance from the x-axis is the y-coordinate of D₁.

(ii) The coordinates of D₁ can be read from the figure. Since it lies on the y-axis, its x-coordinate is 0. The y-coordinate is the vertical distance from the x-axis. From the figure, D₁ is at (0, 2.5).

(iii) R₁

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 local standards and observations.

1. Standard widths for room doors typically range from about 2.5 feet (0.76 m) to 3 feet (0.91 m) or more. Wider doors are preferred for accessibility.

2. This depends on the school. Some schools have wider doors to accommodate wheelchairs, while others may not. Observations and measurements can confirm suitability.

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:

  • Mark point S at (3, -5) in Quadrant IV (x positive, y negative).
  • Mark point Q at (-5, 3) in Quadrant II (x negative, y positive).
  • 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 ≠ y, then (x, y) ≠ (y, x); and (x, y) = (y, x) if and only if x = y. Is this claim true?

Answers:

1. The x-coordinate of any point on the y-axis is 0.

2. Yes, the y-coordinate of any point on the x-axis is 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). They are equal only when x = y.

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