NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.1 2026-27

1. The figure shows Reiaan's room with points O, A, B, and C marking its corners. The x- and y-axes are marked in the figure. Point O is the origin.

Referring to the figure, 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?

Solution: The door begins at point D₁, which lies on the x-axis at a distance of 8 units from the origin O. Therefore, the door is 8 units away from the left wall (the y-axis). As the entire door D₁R₁ lies along the x-axis itself, its distance from the x-axis is 0 units.

(ii) What are the coordinates of D₁?

Solution: Point D₁ lies on the x-axis, so its y-coordinate is 0. It is located 8 units to the right of the origin, giving us the coordinates D₁ = (8, 0).

(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?

Solution: Width of the door = difference of the x-coordinates of R₁ and D₁ = 11.5 − 8 = 3.5 units

Taking 1 unit = 1 foot, the door is 3.5 feet wide. Standard room doors are usually 2 to 3 feet wide, so a 3.5-foot door is more than comfortable. A typical wheelchair measures about 2 to 2.25 feet across, which is well within 3.5 feet — so a person using a wheelchair can enter the room without any difficulty.

(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: Both B₁ and B₂ lie on the y-axis, so the width of the bathroom door = difference between their y-coordinates = 4 − 1.5 = 2.5 units.

The room door is 3.5 units wide, while the bathroom door is only 2.5 units wide. Therefore, the bathroom door is narrower than the room door.

Think and Reflect (NCERT Textbook Page No. 5)

Question 1.
What are the standard widths for a room door? Look around your home and in school.

Solution:
The usual width of a room door is generally between 36 inches and 48 inches, which is about 3 to 4 feet.

Question 2.
Are the doors in your school suitable for people in wheelchairs?

Solution:
Students should observe the doors in their school and check whether they are wide enough for a wheelchair to pass through comfortably.

Think and Reflect (NCERT Textbook Page No. 7)

Question 1.
What is the x-coordinate of a point on the y-axis?

Solution:
The x-coordinate shows the horizontal distance of a point from the y-axis. A point lying on the y-axis has no horizontal distance from it. So, the x-coordinate of every point on the y-axis is 0.

Question 2.
Is there a similar generalisation for a point on the x-axis?

Solution:
Yes. The y-coordinate shows the vertical distance of a point from the x-axis. A point lying on the x-axis has no vertical distance from it. Hence, the y-coordinate of every point on the x-axis is 0.

Question 3.
Does point Q (y, x) ever coincide with point P (x, y)? Justify your answer.

Solution:
Yes, points Q (y, x) and P (x, y) will coincide only when their corresponding coordinates are equal. This means y = x and x = y. Therefore, both points coincide only when x = y.

Question 4.
If x ≠ y, then (x, y) ≠ (y, x); and (x, y) = (y, x) if and only if x = y. Is this claim true?

Solution:
Yes, the claim is true. Two ordered pairs are equal only when their corresponding coordinates are the same. So, (x, y) will be equal to (y, x) only if x = y. If x and y are different, then (x, y) and (y, x) will not be equal.

Why Use Vedantu’s Class 9 Maths Chapter 1 Exercise 1.1 Solutions?

Class 9 Maths Chapter 1 Exercise 1.1 Solutions help students understand how coordinates are used to locate and represent positions. The step-by-step approach makes it easier to follow the method, check answers, and revise Exercise 1.1 confidently.

Key Benefits 

• Understand coordinates: Learn how positions are represented using coordinates.

• Follow each step: Understand the method instead of memorising answers.

• Check your work: Compare your answers and spot mistakes.

• Revise faster: Use the NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.1 for quick revision.

• Practise confidently: Strengthen your understanding through guided practice.

Access Exercise-wise NCERT Solutions for Chapter 1 Maths Class 9

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