# NCERT Solutions for Class 9 Mathematics Chapter 3- Coordinate Geometry

Mathematics is based on  conceptual clarity and proper understanding   of the topics. One can achieve all this if they have the right resources. Extramarks NCERT Solutions for Class 9 Mathematics Chapter 3 is the ultimate guide for students to practice questions and to step up their learning experience and eliminate “mathematics phobia” among students. .

This  Chapter covers topics such as an introduction to the cartesian system, what is an origin, different coordinate axes and quadrants, various points in a quadrant and ways to plot points on a graph.

Our NCERT Solutions for Class 9 Mathematics Chapter 3 is specially designed, keeping in mind all the core concepts of this Chapter. It has highlighted points from the NCERT textbook, making it easier for the students to recall the concepts whenever required. It is based on the latest CBSE syllabus 2021-2022,   prepared by experienced faculty and subject matter experts working conscientiously and diligently to prepare authentic, concise answers which students can trust and enjoy the process of learning.

Extramarks website is a reliable source for NCERT Solutions, NCERT Study materials, Revision notes and Mock tests.

## Key Topics Covered In NCERT Solutions for Class 9 Mathematics Chapter 3

NCERT Solutions Class 9 Mathematics Chapter 3 is the general introduction to the Geometry part of Mathematics. The topics like quadrants and plotting a point on a graph will be beneficial for the students to study the complete unit of Coordinate Geometry in Class 12. . The concepts learnt in this chapter will be applicable in the wide range of Mathematics syllabus in higher classes.

You can find complete details about this chapter in our NCERT Solutions for Class 9 Mathematics Chapter 3. It includes point-to-point coverage  of all the concepts in NCERT Class 9 Mathematics textbook making it convenient to read and apply for the students during their preparation.

The following topics are covered in this chapter

 Exercise Topic 3.1 Introduction 3.2 Cartesian system 3.3 Plotting a point in the plane if its coordinates are given 3.4 Summary

After completing this chapter, students will become better performers in Geometry and it will give tips  to solve all Geometry based problems quickly and easily.  .

3.1 Introduction

This chapter introduces you to the ways you can locate and describe a point in a plane. Recalling the concepts of earlier classes,  how to locate and describe a point on the number line.

Similarly, in this section, you get to know the details about the same for the coordinate Geometry and Cartesian system.

3.2 Cartesian system

You already know that there are fixed points on the number line having positive numbers on the right-hand side whereas negative numbers on the left-hand side.

Likewise, the cartesian system is the representation of the number line with the help of X and Y axes on a graph. The point of intersection of the X and Y axes is a fixed point. This fixed point is called the origin.

To gain in-depth knowledge about the Quadrant, students can get access to our NCERT Solutions for Class 9 Mathematics Chapter 3 by registering on our website.

3.3 Plotting a point in the plane if its coordinates are given

Placing the point in the coordinate system or cartesian system is called plotting a point in the plane. There are a few steps one can follow to plot a point in the plane if its coordinates are given.

Following  steps are  given in  the NCERT Solutions for Class 9 Mathematics Chapter 3:

• Draw a Cartesian system with proper X-axis and Y-axis
• Locate the given coordinates on the cartesian system
• Mark it on the graph paper accordingly
• Draw lines passing through the planes on the respective axes
• Look for their points of intersection
• The point of intersection is the point you have plotted

3.4 Summary

In Coordinate Geometry all the basic applications of Geometry which will be useful in chapters like a circle, parabola and hyperbola in Class 12.

Students should adhere to topics like plotting a point in the plane in order to be thorough in this chapter and develop further  interest in Geometry in  higher classes.

### NCERT Solutions for Class 9 Mathematics Chapter 3 Exercise &  Solutions

Class 9 and Class 10 Mathematics is important for students to understand properly, as it becomes the fundamental basis  for higher  classes. Extramarks  Mathematics faculty experts have created NCERT Solutions for Class 9 Mathematics Chapter 3 to help students prepare for this subject.

Students may  find complete theory and step-by-step solutions to all numerical problems covered in the NCERT textbook. Students should leverage the solution guide to get thorough knowledge and understanding of  the chapter for  Class 9 CBSE examinations.

The solution guide on the Extramarks website for the Class 9 Mathematics Chapter 3 covers topics on basics of the cartesian system, explanation of origin and steps of plotting a point on a graph. Experts advise students to revise this chapter multiple times as it’s a core topic of Geometry. The topics covered in this chapter will go a long way in understanding the advanced level  concepts that would be covered in NCERT Class 10, NCERT Class 11 and NCERT Class 12 Mathematics syllabus.

Click on the  links given below to view exercise specific questions and  NCERT Solutions for Class 9 Mathematics Chapter 3.

• Chapter 3: Exercise 3.1 – Question and Answer Solutions
• Chapter 3: Exercise 3.2 – Question and Answer Solutions
• Chapter 3: Exercise 3.3- Question and Answer Solutions

By choosing Extramarks, students can enjoy a smooth and complete learning experience. NCERT Solutions for Class 9 Mathematics Chapter 3 is written in very easy language. It is designed after extensive research and following the CBSE syllabus and  previous years CBSE question papers.

Along with Chapter 3 Mathematics Class 9 Solutions, you can explore NCERT Solutions on our Extramarks website for all primary and secondary classes.

• NCERT Solutions Class 1
• NCERT Solutions Class 2
• NCERT Solutions Class 3
• NCERT Solutions Class 4
• NCERT Solutions Class 5
• NCERT Solutions Class 6
• NCERT Solutions Class 7
• NCERT Solutions Class 8
• NCERT Solutions Class 9
• NCERT solutions Class 10
• NCERT solutions Class 11
• NCERT solutions Class 12

### NCERT Exemplar Class 9  Mathematics

NCERT Exemplar Class 9 Mathematics is a complete source of information for CBSE students preparing for their  grade 9  exams. It consists of various examples of helping students to leverage their performance. While revising from NCERT Exemplars, students gather complete knowledge of the Mathematics concepts and gain deeper insights on a variety of interconnected  topics between various chapters.

Exemplar books have proved not only beneficial for students in CBSE but also in other curriculum. It covers complex theories that confidently prepare students to face the upcoming examinations. Students appearing for Class 9 are advised to refer to the NCERT Exemplar Class 8 Mathematics and involve it in their core study materials. Students will get a deeper knowledge of solving complex queries, and it will help prepare them for boards and other entrance examinations.

After referring to the NCERT Solutions and NCERT Exemplar, the students will be able to think logically about a problem. Then they may switch  to more advanced and higher-level conceptual questions.

#### Key Features of NCERT Solutions for Class 9 Mathematics Chapter 3

It is necessary that students have the right and handy study resources to learn from and score well in exams. Therefore, NCERT Solutions for Class 9 Mathematics Chapter 3 offers a complete solution for all problems. The key features provided are:

• Extramarks NCERT Solutions for Class 9 Mathematics Chapter 3 helps students to retain whatever they have learnt for a long time
• The core concepts covered in Extramarks NCERT Solutions for Class 9 Mathematics Chapter 3 will aid students to excel in their school examinations.
• Students will learn ways to solve all the numerical with great speed and  accuracy
• With the Coordinate Geometry chapter solutions, students will be able to apply the concepts  required to solve many Geometry related problems.

Q.1 How will you describe the position of a table lamp on your study table to another person?

Ans-

Consider the lamp as a point and table as a plane. Choose any two perpendicular edges of the table. Measure the distance of the lamp from the longer edge, suppose it is 25 cm. Again, measure the distance of the lamp from the shorter edge, and suppose it is 30 cm. You can write the position of the lamp as (30, 25) or (25, 30), depending on the order you fix. Q.2 (Street Plan): A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction. All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city on your note book. Represent the roads/streets by single lines.

There are many cross- streets in your model. A particular cross-street is made by two streets, one running in the North – South direction and another in the East – West direction. Each cross street is referred to in the following manner. If the 2nd street running in the North – South direction and 5th in the East – West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:

(i) how many cross – streets can be referred to as (4, 3).

(ii) how many cross – streets can be referred to as (3, 4).

Ans-

The street plan according to given instruction is given below: (i) Two cross – streets can be referred to as (4, 3).
(ii) Two cross – streets can be referred to as (3, 4).

Q.3 Write the answer of each of the following questions:

(i) What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?

(ii) What is the name of each part of the plane formed by these two lines?

(iii) Write the name of the point where these two lines intersect.

Ans-

(i) The name of horizontal line is x-axis and the name of vertical line is y-axis in the Cartesian plane.

(ii) The name of each part of the plane formed by these two lines is quadrant.

(iii) The name of the point where these two lines intersect is the origin.

Q.4 See Fig.3.14, and write the following:
(i) The coordinates of B.
(ii) The coordinates of C.
(iii) The point identified by the coordinates (–3, –5).
(iv) The point identified by the coordinates (2, – 4).
(v) The abscissa of the point D.
(vi) The ordinate of the point H.
(vii) The coordinates of the point L.
(viii) The coordinates of the point M. Ans-

(i) Coordinate of B is (–5, 2).
(ii) Coordinate of C is (5, –5).
(iii) The point identified by the coordinates (–3, –5) is E.
(iv) The point identified by the coordinates (2, –4) is G.
(v) The abscissa of the point D is 6.
(vi) The ordinate of the point H is –3.
(vii) The coordinates of the point L is (0, 5).
(viii) The coordinates of the point M is (–3, 0).

Q.5 In which quadrant or on which axis do each of the points (– 2, 4), (3, – 1), (– 1, 0), (1, 2) and (– 3, – 5) lie? Verify your answer by locating them on the Cartesian plane.

Ans-

The positions of the given coordinates are given below:

 Coordinate Location in cartesian plane (– 2, 4) Second quadrant (3, – 1) Fourth quadrant (– 1, 0) On X-axis (1, 2) First quadrant (– 3, – 5) Third quadrant

Graphical representation of the coordinates is given below: Q.6 Plot the points (x, y) given in the following table on the plane, choosing suitable units of distance on the axes.

 x –2 –1 0 1 3 y 8 7 –1.25 3 –1

Ans-

The graphical representation of the points is given below: 