NCERT Solutions for Class 9 Maths Chapter 3: Coordinate Geometry

The NCERT (National Council of Educational Research and Training) textbook for Class 9 Maths introduces Coordinate Geometry as a foundational tool for higher mathematics. This chapter bridges the gap between basic arithmetic and visual algebra. By following the CBSE Class 9 Maths syllabus, these solutions ensure that learners understand the relationship between a number line and a two-dimensional plane.

In the NCERT Solutions for Class 9 Coordinate Geometry serves as the vital link between Algebra and Geometry. While basic geometry deals with shapes, coordinate geometry allows us to locate points and describe those shapes using numbers. This system was pioneered by the mathematician René Descartes, which is why we refer to it as the Cartesian System.

The Origin and the Number Line: In previous chapters, students learned to represent numbers on a single line. Chapter 3: Coordinate Geometry expands this by intersecting two perpendicular number lines. The horizontal line is defined as the X-axis, and the vertical line is the Y-axis. Their point of intersection is called the Origin, denoted by the coordinates (0,0).

Download NCERT Solutions Class 9 Maths Chapter 3 PDF

Access our comprehensive, free NCERT Solutions for Class 9 Maths Chapter 3: Coordinate Geometry in PDF format. These solutions are professionally drafted to simplify the Cartesian System and help students align with the latest CBSE marking schemes.

What is Covered in Class 9 Coordinate Geometry?

Our solutions focus on the core competencies required by the CBSE Class 9 syllabus, ensuring students build a foundation for higher-level geometry. Key learning outcomes include:

• The Cartesian Plane: Understanding the intersection of the horizontal X-axis and the vertical Y-axis.
• Locating Points: Mastering the use of Ordered Pairs (x,y) to define a point's exact position.
• Quadrant Identification: Learning the sign conventions (+,+), (−,+), (−,−), (+,−) to determine which of the four Quadrants a point occupies.
• Terminological Mastery: Defining the Abscissa (x-value) and the Ordinate (y-value) with precision.
• Axis Points: Identifying why points with a zero coordinate (e.g., (5,0) or (0,−2)) lie on the Axes rather than within a quadrant.
• Practical Graphing: Bridging the gap between algebraic coordinates and visual representation on a graph sheet.

Why Practice Infinity Learn NCERT Solutions for Class 9?

Consistent engagement with these NCERT Class 9 Coordinate Geometry questions allows students to identify conceptual gaps early. By mastering the ability to plot points accurately, students prepare themselves for Chapter 4 (Linear Equations) and improve their speed and accuracy for the final CBSE examinations.

NCERT Solutions for Class 9 Maths Coordinate Geometry Exercise 

These NCERT Solutions for Class 9 Maths prioritize the logic behind the plotting.

NCERT Solutions for Class 9 Maths Chapter 3 Exercise 3.1

Question1. How will you describe the position of a mobile phone kept on the study table to another person?

Answer:

For describing the position of a mobile phone kept on the study table, we take two lines, a perpendicular and a horizontal line. Considering the table as a plane (x and y axis) and taking perpendicular line as Y axis and horizontal as X axis respectively. Take one corner of table as origin where both X and Y axes intersect each other. Now, the length of table is Y axis and breadth is X axis. From The origin, join the line to the mobile phone and mark a point. The distances of the point from both X and Y axes should be calculated and then should be written in terms of coordinates.

Let the distance of the point from X- axis and Y- axis is x and y respectively, so the mobile phone will be in (x, y) coordinate.

Question 2: Street Plan: There are 2 main roads in a city. They intersect each other, at the center of the city. East-West and North-South are the directions of the two roads. Rest streets of the city are at 200 m from each other and are parallel to these roads. There are (five) streets in every direction. Using 1cm = 200 m as scaling unit, draw a model of the city. Representation of roads/streets will be given by single lines. A model which has cross streets in which one particular cross street is made by 2 streets in which one running from North to South direction and the other runs from the East to the West direction. Each of these cross streets are referred as in the following manner: Through which the second street runs from the north to the south and the fifth runs from the East to the West which meets at some crossing, then the cross street that intersect each other will be (2,5). Using this convention, Find:

(1) How many cross – streets can be referred to as (4, 3).

(2) How many cross – streets can be referred to as (3, 4).

Answer:

(1) Only one street can be referred to as (4, 3) (as clear from the figure).

(2) Only one street can be referred to as (3, 4) (as we see from the figure).

NCERT Solutions for Class 9 Maths Chapter 3 Exercise 3.2

Question 1: Answer the following questions:

(1) Name the horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?

(2) Name each part of the plane formed by the above two lines?

(3) Name the point where these two lines intersect.

Answer:

(1) The name of horizontal and vertical lines drawn to determine the position of any point in the Cartesian plane is x-axis and y-axis respectively.

(2) The name of each part of the plane formed by these two lines x-axis and y-axis is quadrants.

(3) The point where these two lines intersect is called origin.

Question 2: Answer the following referring to the figure given below:

(1) co-ordinates of B.

(2) co-ordinates of C.

(3) co-ordinates of the point L.

(4) co-ordinates of the point M.

(5) ordinate of the point H.

(6) abscissa of the point D.

(7) The point i.e., identified by the co-ordinates (−3, −5).

(8) The point i.e., identified by the co-ordinates (2, −4).

Answer:

(1) The co-ordinates of B are (−5, 2).

(2) The co-ordinates of C are (5, −5).

(3) The co-ordinates of the point L are (0, 5).

(4) The co-ordinates of the point M are (−3, 0).

(5) Ordinate means y coordinate of point H. So, ordinate of point H is -3.

(6) Abscissa means x co-ordinate of point D. So, abscissa of the point D is 6.

(7) The point identified by the coordinates (−3, −5) is E.

(8) The point identified by the coordinates (2, −4) is G.

NCERT Solutions for Class 9 Maths Chapter 3 Exercise 3.3

Question 1. Represent the following points (3, −1), (−2, 4), (1, 2), (−1, 0) and (−3, −5) on a Cartesian plane and also tell in which quadrant do they lie? Give reason for your answer.

Answer:

First, we draw all points on the Cartesian plane.

From the figure, we can find that:

(−2, 4) lies in Second quadrant.

(3, −1) lies in Fourth quadrant.

(−1, 0) lies in Second quadrant.

(1, 2) lies in First quadrant.

(−3, −5) lies in Third quadrant.

Question 2: Plot the points (x, y) given in the following table on the plane, choosing suitable units of distance on the axes and also tell in which quadrant or axis does it lies.

Answer:

Points (x, y) on the plane.

Here, let 1unit = 1 cm

First, we draw all the given points on the Cartesian plane.

From the figure, we find that:

(−2, 8) lies in Second quadrant.

(−1, 7) lies in Second quadrant.

(0, −1.25) lies in Fourth quadrant.

(1, 3) lies in First quadrant.

(3, −1) lies in Fourth quadrant.