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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.

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Quick Information Box

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

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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.

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Important Formulas

Coordinates of Origin

O = (0, 0)

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Point on x-axis

(x, 0)

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Point on y-axis

(0, y)

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Distance Formula

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

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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.

Question 1

If D₁R₁ represents the door to Reiaan’s room:

(i) How far is the door from the left wall (y-axis)? How far is the door from the x-axis?

Solution

From Fig. 1.3, the door lies on the x-axis.

Therefore:

Distance from y-axis = 10 units

Distance from x-axis = 0 units

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(ii) What are the coordinates of D₁?

Solution

From the figure:

D₁ = (10, 0)

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(iii) If R₁ is the point (11.5, 0), how wide is the door?

Solution

Width of door:

= 11.5 − 10
= 1.5 units

Therefore:

Door width = 1.5 ft

This is comfortable for normal use but may be narrow for wheelchair access.

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(iv) If B₁ (0, 1.5) and B₂ (0, 4) represent bathroom door ends, is bathroom door narrower or wider?

Solution

Bathroom door width:

= 4 − 1.5
= 2.5 units

Therefore:

Bathroom door is wider.

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Question 2

Are school doors suitable for wheelchairs?

Solution

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

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Important Observation

Coordinates Rule

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

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

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Common Mistakes

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

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Exam Tips

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

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Practice MCQs

MCQ 1

Coordinates of origin are:

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

Answer:

C. (0, 0)

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MCQ 2

A point on x-axis has:

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

Answer:

B. y = 0

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MCQ 3

The coordinate plane is divided into:

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

Answer:

C. 4 quadrants

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MCQ 4

The horizontal axis is called:

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

Answer:

C. x-axis

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FAQ Section

What is the origin in coordinate geometry?

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

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What are coordinates of origin?

(0, 0)

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What is the x-axis?

The horizontal axis is called the x-axis.

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Why is Exercise 1.1 important?

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

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