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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.

1.4 DISTANCE BETWEEN TWO POINTS IN THE 2-D PLANE

This section explains how to find the distance between any two points in the Cartesian plane, not just those lying on the axes or parallel to them. Using the Baudhayana–Pythagoras theorem (the Pythagorean theorem), the distance between two points (x1, y1) and (x2, y2) is derived.

By considering the horizontal and vertical distances between the points as the legs of a right triangle, the distance between the points is the hypotenuse. For example, for points A (3, 4) and D (7, 1), the horizontal distance is |7 - 3| = 4 units, and the vertical distance is |4 - 1| = 3 units. Applying the theorem, the distance AD = √(4² + 3²) = 5 units.

This method generalizes to any two points, regardless of their position in the plane or the signs of their coordinates. The formula for the distance between points (x1, y1) and (x2, y2) is:

Distance = √[(x2 - x1)² + (y2 - y1)²]

The section also discusses reflections of triangles across axes, showing that distances remain unchanged, illustrating the concept of congruence and symmetry in the plane.

Students are encouraged to think about how distances along axes relate to the total distance and to explore the effects of reflections on coordinates and distances.

📊 Diagram: Fig. 1.6: Triangle ADM; Fig. 1.7: Right triangle illustrating distances; Fig. 1.8: Distance formula illustration; Fig. 1.9: Reflection of triangle ADM in y-axis

🧪 Activity: Think and Reflect questions on distances moved along axes and effects of reflection.

🔗 Connection: Prepares for end-of-chapter exercises involving plotting, distance calculations, and coordinate geometry applications.

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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