NCERT Class 9 Maths Exercise 1.1 Solutions | Coordinate Geometry NCERT Solutions

Short Intro

In this post, students can find complete step-by-step solutions for Class 9 Maths Chapter 1 Exercise 1.1 – Orienting Yourself: The Use of Coordinates. All questions are solved in simple language with proper explanations based on the latest NCERT syllabus to help students understand coordinate geometry easily.

Quick Information Box

Item Details
Board NCERT / CBSE
Class 9
Subject Maths
Chapter Coordinate Geometry
Exercise 1.1
Topic Cartesian Coordinate System

Concepts Used (Topics Covered)

  • Cartesian Coordinate Plane
  • x-axis and y-axis
  • Coordinates of a Point
  • Origin
  • Positive and Negative Directions
  • Distance on Coordinate Plane
  • Practical Applications of Coordinates

The exercise introduces the coordinate system and coordinates of points on the plane.

Important Formulas

Coordinates of Origin

O = (0, 0)

Point on x-axis

(x, 0)

Point on y-axis

(0, y)

Distance Formula

(x2−x1)2+(y2−y1)2\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Questions & Step-by-step Solutions

Following Figure shows Reiaan’s room with points OABC marking its corners. The
x- and y-axes are marked in the figure. Point O is the origin.

image

Question 1

If D₁R₁ represents the door to Reiaan’s room:

(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 doorfrom the x-axis?

Solution

(ii) What are the coordinates of D₁?

Solution

(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

(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

Think and Reflect

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

The standard width of a room door is usually:

  • 75 cm (2.5 feet) for small rooms
  • 80 cm (about 2.6 feet) for most bedrooms and living rooms
  • 90 cm (3 feet) for larger rooms and main entrances

In many homes and schools, you will commonly find doors that are 80–90 cm wide.

Activity

Look around your home and school and measure a few doors. You may observe:

Place Approximate Door Width
Bedroom 75–80 cm
Bathroom 60–75 cm
Classroom 90–120 cm
Main Entrance 90–120 cm

You can use a measuring tape to check the actual widths and compare them with these standard sizes.

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

Solution

Modern accessibility standards recommend wider doors for wheelchair users. Schools should ideally have ramps and wide doors for easy movement.

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

x-coordinate of a point on the y-axis is always 0.
Example: (0, 5), (0, −3)

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

Yes. For a point on the x-axis, the y-coordinate is always 0.
Example: (4, 0), (−2, 0)

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

Q(y, x) coincides with P(x, y) only when x = y.
Because both coordinates must be same:
(x, y) = (y, x) ⇒ x = y.

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

Yes, the claim is true.
If x ≠ y, then swapping coordinates changes the point, so (x, y) ≠ (y, x).
And (x, y) = (y, x) only when x = y.

Answer : 0

Important Observation

Coordinates Rule

A point on x-axis has y-coordinate = 0
A point on y-axis has x-coordinate = 0

Common Mistakes

  • Interchanging x-coordinate and y-coordinate
  • Forgetting sign conventions
  • Confusing axes
  • Incorrect distance calculation

Exam Tips

  • Always write coordinates in form (x, y).
  • x-coordinate is written first.
  • Learn positive and negative directions properly.
  • Practice plotting points regularly.

Practice MCQs

MCQ 1

Coordinates of origin are:

A. (1, 0)
B. (0, 1)
C. (0, 0)
D. (1, 1)

Answer:

C. (0, 0)

MCQ 2

A point on x-axis has:

A. x = 0
B. y = 0
C. x = y
D. None

Answer:

B. y = 0

MCQ 3

The coordinate plane is divided into:

A. 2 quadrants
B. 3 quadrants
C. 4 quadrants
D. 5 quadrants

Answer:

C. 4 quadrants

MCQ 4

The horizontal axis is called:

A. y-axis
B. origin
C. x-axis
D. quadrant

Answer:

C. x-axis

FAQ Section

What is the origin in coordinate geometry?

The point where x-axis and y-axis intersect is called the origin.

What are coordinates of origin?

(0, 0)

What is the x-axis?

The horizontal axis is called the x-axis.

Why is Exercise 1.1 important?

It forms the foundation of coordinate geometry used in higher mathematics.

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