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Coordinate geometry is the study of geometrical figures that link algebra and geometry by defining points on the axes. The other name of coordinate geometry is analytic geometry or Cartesian geometry. Coordinate geometry helps to determine the distance between two points on the coordinate axes. Coordinate geometry is the study of algebraic equations on a graph. Coordinate geometry is used in many areas, like determining the distance between two places to determine the area of a triangle in the Cartesian plane, determining the midpoint of a line, in GPS, determining the longitude and latitude, forecasting, storms' exact location, etc.
This Story also Contains
- NCERT Class 9 Maths Chapter 3 Coordinate Geometry: Notes
- Cartesian System
- Class 9 Chapter Wise Notes
- NCERT Solutions for Class 9
- NCERT Exemplar Solutions for Class 9
- NCERT Books and Syllabus
These notes included the definition of coordinate geometry and the Cartesian system. What are the origin, coordinate axes and quadrants? How to plot points and make a line on a graph? CBSE Class 9 chapter Coordinate Geometry includes all the topics and their examples in these notes. Our experts designed NCERT class 9th maths notes that will help the students to understand the concepts easily. NCERT notes cover all the chapters according to the latest syllabus of NCERT.
NCERT Class 9 Maths Chapter 3 Coordinate Geometry: Notes
Coordinate Geometry: It is an analytical geometry that is used for defining the exact position of a point using coordinates.
Cartesian System
The Cartesian system is a method of defining the position of a point in a plane. In this method, points are located using two perpendicular lines. In the Cartesian system, the horizontal line is called the X-axis and it is represented by XX', and the vertical line is called Y- axis and it is represented by YY'.
Origin
The place where the two perpendicular lines of the X-axis and the Y-axis intersect is called the origin, and it is denoted by the letter $O$. This origin divides the line into positive and negative directions as OX and OY are called the positive direction, and OX' and OY' are called the negative direction of the graph.
Coordinate Axes and Quadrants
The origin divides the plane into four sections, and these sections are known as quadrants. Quadrants are numbered as I, II, III and IV in an anticlockwise direction starting from the top right section. The plane where these quadrants exist is called the Cartesian plane, coordinate plane or XY plane and the axes on this Cartesian plane are called coordinate axes.
Points in Different Quadrants
The four quadrants in the XY plane are as follows,
Quadrant I: It is represented by (+, +) signs, which means X and Y are both positive.
Example: (2, 7)
Quadrant II: It is represented by (–, +) signs, which means X is negative and Y is positive.
Example: (-3, 4)
Quadrant III: It is represented by (–, –) signs, which means X and Y are both negative.
Example: (-4,-4)
Quadrant IV: It is represented by (+, –) signs, which means X is positive and Y is negative.
Example: (1, -9)
Plotting on a Graph
On the plane, a set of numbers or coordinates is given to define the position of the point in the XY plane, and these coordinate points are represented by an ordered pair of (x, y) where, X or distance from origin to X axis is called abscissa or X-coordinate and the distance from O to Y axis is called the ordinate or Y-coordinate as shown in figure.
Plotting a Point in the Plane if Its Coordinates Are Given
In the coordinate plan, the X-coordinate implies that the distance from the origin to the X-axis and the Y-coordinate implies that the distance from the origin to the Y-axis. These points can be:
Example: Plot the coordinates (1, 2), (2, -4), (-3, 4) and (-2, -2) in the Cartesian plane.
Here,
(1, 2)→It is 1 unit away from the positive y-axis and 2 units away from the positive x-axis.
(2, -4)→It is 2 units away from the positive y-axis and 4 units away from the negative x-axis.
(-3, 4)→It is 3 units away from the negative y-axis and 4 units away from the positive x-axis.
(-2, -2)→It is 2 units away from the negative y-axis and 2 units away from the negative x-axis.
The plotting of these coordinates is shown in the figure:
Class 9 Chapter Wise Notes
Students must download the notes below for each chapter to ace the topics.
NCERT Notes for Class 9 Maths Chapter 3 - Coordinate Geometry |
NCERT Notes for Class 9 Maths Chapter 4 - Linear Equations in Two Variables |
NCERT Notes for Class 9 Maths Chapter 5 - Introduction to Euclid’s Geometry |
NCERT Notes for Class 9 Maths Chapter 11 - Surface Areas and Volumes |
NCERT Solutions for Class 9
Students must check the NCERT solutions for Class 10 Maths and Science given below:
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Students must check the NCERT exemplar solutions for Class 10 Maths and Science given below:
NCERT Books and Syllabus
To learn about the NCERT books and syllabus, read the following articles and get a direct link to download them.
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