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Short Intro

In this post, students can find complete step-by-step solutions for Class 9 Maths Chapter 1 Exercise 1.2 – Coordinate Geometry. All questions are solved in simple language with proper explanations based on the latest NCERT syllabus to help students understand coordinates, quadrants, plotting points, and practical applications of coordinate geometry easily.

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Quick Information Box

Item	Details
Board	NCERT / CBSE
Class	9
Subject	Maths
Chapter	Coordinate Geometry
Exercise	1.2
Topic	Cartesian Plane & Coordinates

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Concepts Used (Topics Covered)

• Cartesian Coordinate System
• Coordinates of Points
• Quadrants
• Plotting Points
• Rectangular Shapes on Coordinate Plane
• Distance Along Axes
• Coordinates in Real Life

The exercise explains how coordinates help locate objects precisely in the Cartesian 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

On a graph sheet, mark the x-axis and y-axis and the origin O. Mark
points from (– 7, 0) to (13, 0) on the x-axis and from (0, – 15) to (0, 12) on
the y-axis. (Use the scale 1 cm = 1 unit.) Using Fig. 1.5, answer the given
questions.

Question 1

Place reiaan’s rectangular study table has three feet at points (8, 9), (11, 9), and (11, 7).

(i) Where will the fourth foot of the table be?

Solution

The table is rectangular.

Given points:

(8, 9), (11, 9), (11, 7)

The missing point will be:

(8, 7)

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(ii) Is this a good spot for the table?

Solution

Yes, the table is placed neatly beside the bed and leaves enough walking space.

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(iii) What is the width and length of the table?

Solution

Length:

11 − 8 = 3 ft

Width:

9 − 7 = 2 ft

Therefore:

Length = 3 ft
Width = 2 ft

The height cannot be determined from a 2-D floor plan.

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Question 2

If the bathroom door opens into the bedroom, will it hit the wardrobe?

Solution

No, according to the diagram, the bathroom door will not hit the wardrobe because sufficient space is available between them.

If the door is made wider, it should open outward or the wardrobe should be shifted slightly.

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Question 3

Look at Reiaan’s bathroom.

(i) What are the coordinates of corners O, F, R and P?

Solution

From the figure:

O = (0, 0)
F = (0, 10)
R = (−7, 10)
P = (−7, 0)

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(ii) What is the shape of showering area SHWR?

Solution

The showering area is rectangular.

Coordinates:

S = (−7, 5)
H = (−4, 5)
W = (−4, 10)
R = (−7, 10)

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(iii) Mark 3 ft × 2 ft washbasin area and 2 ft × 3 ft toilet area.

Solution

One possible answer:

Washbasin coordinates:

(−7, 8), (−5, 8), (−5, 10), (−7, 10)

Toilet coordinates:

(−7, 0), (−5, 0), (−5, 3), (−7, 3)

(Answers may vary.)

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Question 4

Reiaan’s room door leads to the dining room of length 18 ft and width 15 ft.

(i) Sketch the dining room and mark coordinates.

Solution

One possible set of coordinates:

P = (−7, 0)
A = (12, 0)
B = (12, 15)
C = (−7, 15)

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(ii) Place a rectangular 5 ft × 3 ft dining table at the centre.

Solution

Possible coordinates:

(0, 6), (5, 6), (5, 9), (0, 9)

(Answers may vary.)

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Important Observation

Coordinates in Different Quadrants

Quadrant I  → (+, +)
Quadrant II → (−, +)
Quadrant III → (−, −)
Quadrant IV → (+, −)

The coordinate plane is divided into four quadrants.

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Common Mistakes

• Writing coordinates in wrong order
• Confusing x-axis and y-axis
• Forgetting negative signs
• Incorrect plotting of points
• Confusing length and width

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Exam Tips

• Always write coordinates in form (x, y).
• Practice plotting points regularly.
• Learn quadrant signs carefully.
• Use graph paper neatly during exams.

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Practice MCQs

MCQ 1

Coordinates of origin are:

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

Answer:

B. (0, 0)

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MCQ 2

Point (−3, 5) lies in:

A. Quadrant I
B. Quadrant II
C. Quadrant III
D. Quadrant IV

Answer:

B. Quadrant II

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MCQ 3

A point on y-axis has:

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

Answer:

A. x = 0

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MCQ 4

Coordinates are always written as:

A. (y, x)
B. (x, y)
C. x + y
D. x − y

Answer:

B. (x, y)

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FAQ Section

What is a Cartesian plane?

The plane formed by x-axis and y-axis is called the Cartesian plane.

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How many quadrants are there?

There are four quadrants in the coordinate plane.

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What are coordinates of origin?

(0, 0)

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Why is Exercise 1.2 important?

It helps students understand plotting points and coordinate geometry used in higher mathematics.

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Source

Class 9 Maths Chapter 1 – Coordinate Geometry Exercise 1.2