Class 9 Mathematics Exercise-3.1 & 3.2 NCERT Solutions Olympiad Board Exam

Chapter 3

Coordinate Geometry

Step-by-step NCERT solutions with stress–strain analysis and exam-oriented hints for Boards, JEE & NEET.

4 Questions

10–15 min Ideal time

Q1 Now at

📘 Concept & Theory Describing Coordinates ›

Coordinate Geometry helps us describe the exact position of an object using two perpendicular directions. A fixed point called the origin is selected, and distances are measured along:

x-axis → Horizontal direction
y-axis → Vertical direction
Every position is represented in the form: \[ (x,y) \]
Here, \[ x=\text{horizontal distance} \] and \[ y=\text{vertical distance} \]

📊 Graph / Figure Graph / Figure ›

Fig. 1 — Free body diagram

🗺️ Solution Roadmap Step-by-step Plan ›

Choose a fixed corner of the table as the origin.
Consider two perpendicular edges of the table as coordinate axes.
Measure the horizontal distance of the lamp from the origin.
Measure the vertical distance of the lamp from the origin.
Write both distances in the form: \[\small (x,y)\]

✏️ Solution Complete Solution ›

To describe the position of the table lamp, we use the idea of coordinates.

First, consider the surface of the study table as a flat plane.
Choose one corner of the table as the origin: \[ (0,0) \]
The horizontal edge of the table represents the: \[ x\text{-axis} \] and the vertical edge represents the: \[ y\text{-axis} \]
Measure the horizontal distance of the lamp from the origin. Suppose it is: \[ 30\text{ cm} \]
Measure the vertical distance of the lamp from the origin. Suppose it is: \[ 20\text{ cm} \]
Therefore, the coordinates of the lamp are: \[ (30,20) \]
Hence, we can say:

“The lamp is placed 30 cm along the horizontal direction and 20 cm along the vertical direction from the chosen corner of the table.”

🎯 Exam Significance Exam Significance ›

This question builds the basic understanding of locating points in Coordinate Geometry.
It is important for board examinations because students must understand how coordinates represent positions.
Competitive entrance examinations frequently ask questions related to plotting points, locating positions, and interpreting coordinates.
This concept is also used in Physics, Computer Graphics, Navigation Systems, and Engineering Mathematics.

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1 / 4 · 25%

Q2 →

NUMERIC3 marks

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 notebook. 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)

📘 Concept & Theory City Plan ›

In Coordinate Geometry, the position of a point is uniquely determined by an ordered pair: \[ (x,y) \]

The first number represents the position along one direction.
The second number represents the position along the perpendicular direction.
Since the order of numbers matters, \[ (4,3)\neq(3,4) \]
Every pair of streets intersects at exactly one unique point.

📊 Graph / Figure Graph / Figure ›

Fig-1 : Model of the City Showing Cross-Streets

🗺️ Solution Roadmap Step-by-step Plan ›

Understand that each crossing is represented by an ordered pair.
The first number represents the North-South street.
The second number represents the East-West street.
Identify the intersection corresponding to each ordered pair.
Observe that each ordered pair gives exactly one unique crossing.

✏️ Solution Complete Solution ›

From the city model shown above, every crossing point is represented by an ordered pair: \[\small (x,y)\]

Here,

The first number represents the North-South street.
The second number represents the East-West street.

(i) Cross-street referred to as \(\small (4,3)\)

The ordered pair: \[\small (4,3)\] means:

4th street in the North-South direction
3rd street in the East-West direction

These two streets intersect at exactly one point.

Therefore,

There is one and only one cross-street referred to as: \[\small (4,3)\]

(ii) Cross-street referred to as \(\small (3,4)\)

The ordered pair: \[\small (3,4)\] means:

3rd street in the North-South direction
4th street in the East-West direction

These two streets also intersect at exactly one point.

Therefore,

There is one and only one cross-street referred to as: \[\small (3,4)\]

🎯 Exam Significance Exam Significance ›

This question develops the concept of ordered pairs and location of points.
It helps students understand that: \[ (a,b)\neq(b,a) \]
Questions based on coordinates, grids, and plotting points are frequently asked in school examinations.
Similar concepts are widely used in maps, GPS systems, computer graphics, and engineering applications.
Competitive examinations often test interpretation of coordinate systems and spatial reasoning.

← Q1

2 / 4 · 50%

Q3 →

NUMERIC3 marks

Exercise 3.2

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

📘 Concept & Theory Cartesian Plane ›

A Cartesian Plane is formed by two perpendicular number lines. These lines help us locate the exact position of points on a plane.

The horizontal line is called the: \[ x\text{-axis} \]
The vertical line is called the: \[ y\text{-axis} \]
These two axes divide the plane into four parts called: \[ \text{Quadrants} \]
The point where the two axes intersect is called the: \[ \text{Origin} \]

📊 Graph / Figure Graph / Figure ›

Fig-1 : Cartesian Plane Showing Axes, Origin and Quadrants

🗺️ Solution Roadmap Step-by-step Plan ›

Identify the horizontal line of the Cartesian plane.
Identify the vertical line of the Cartesian plane.
Observe how these two lines divide the plane into parts.
Determine the special point where both lines intersect.

✏️ Solution Complete Solution ›

(i) Name of horizontal and vertical lines

The horizontal line is called the: \[\small x\text{-axis}\]

The vertical line is called the: \[\small y\text{-axis}\]

Answer: \[\small x\text{-axis and } y\text{-axis}\]

(ii) Name of each part formed by these lines

The x-axis and y-axis divide the Cartesian plane into four parts.

Each part is called a: \[\small \text{Quadrant}\]

Answer: \[\small \text{Quadrants}\]

(iii) Name of the point where these two lines intersect

The x-axis and y-axis intersect at a fixed point: \[\small (0,0)\]

This point is called the: \[\small \text{Origin}\]

Answer: \[\small \text{Origin}\]

🎯 Exam Significance Exam Significance ›

This question develops the basic understanding of the Cartesian coordinate system.
Concepts of x-axis, y-axis, origin, and quadrants are fundamental for all future Coordinate Geometry chapters.
Questions based on quadrants and coordinate planes are frequently asked in board examinations.
Competitive examinations often include graph interpretation and coordinate-based reasoning.
These concepts are also important in Physics, Computer Graphics, Engineering, and Navigation Systems.

← Q2

3 / 4 · 75%

Q4 →

📘 Concept & Theory Coordinates ›

Every point on the Cartesian plane is represented by an ordered pair: \[\small (x,y)\]

The first number is called the: \[\small \text{Abscissa}\] which represents the distance along the x-axis.
The second number is called the: \[\small \text{Ordinate}\] which represents the distance along the y-axis.
Positive values are measured in the positive direction of the axes and negative values in the opposite direction.
To locate a point:

Move horizontally first, then vertically.

📊 Graph / Figure Graph / Figure ›

Fig-3.14 : Cartesian Plane Showing Coordinates of Different Points

🗺️ Solution Roadmap Step-by-step Plan ›

Observe the position of each point on the graph.
Read the horizontal distance from the origin to get the abscissa.
Read the vertical distance from the origin to get the ordinate.
Write the coordinates in the form: \[\small (x,y)\]
Carefully note the signs of the coordinates according to the quadrant.

✏️ Solution Complete Solution ›

The coordinates of point B

Point B lies:
- 5 units left of the origin \[\small x=-5\]
- 2 units above the origin \[\small y=2 \]
Therefore, the coordinates of B are: \[\small (-5,2) \]
The coordinates of point C

Point C lies:
- 5 units right of the origin \[\small x=5 \]
- 5 units below the origin \[\small y=-5 \]
Therefore, \[\small C=(5,-5) \]
Point identified by coordinates \((-3,-5)\)

On the graph, the point having coordinates: \[\small (-3,-5) \] is point: \[\small E \]

Therefore, the required point is: \[\small E \]
Point identified by coordinates \(\small (2,-4)\)

On the graph, the point having coordinates: \[\small (2,-4) \] is point: \[\small G \]

Therefore, the required point is: \[\small G \]
Abscissa of point D

The abscissa means the x-coordinate.

Point D lies 6 units to the right of the origin.

Therefore, the abscissa of D is: \[\small 6 \]
Ordinate of point H

The ordinate means the y-coordinate.

Point H lies 3 units below the x-axis.

Therefore, the ordinate of H is: \[\small -3 \]
Coordinates of point L

Point L lies:
- On the y-axis \[\small x=0 \]
- 5 units above the origin \[\small y=5 \]
Therefore, \[\small L=(0,5) \]
Coordinates of point M

Point M lies:
- 3 units left of the origin \[\small x=-3 \]
- On the x-axis \[\small y=0 \]
Therefore, \[\small M=(-3,0) \]

🎯 Exam Significance Exam Significance ›

This question develops accuracy in reading coordinates from a graph.
Students learn the concepts of: \[ \text{Abscissa and Ordinate} \]
Board examinations frequently ask graph-based coordinate questions.
Competitive examinations test quadrant identification and coordinate interpretation.
These concepts form the foundation for advanced geometry, graph plotting, trigonometry, and analytical geometry.

← Q3

4 / 4 · 100%

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Chapter Complete!

All 4 solutions for Coordinate Geometry covered.

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Coordinate Geometry

Exercise 3.1

Exercise 3.2

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