CBSE Class 9 Maths Chapter 1 - Orienting Yourself: The Use of Coordinates Notes
These CBSE Class 9 Maths Notes are based on the latest CBSE syllabus and revised NCERT Ganita Manjari textbook. They cover important concepts, formulas, solved examples, and key points for easy revision, homework, practice, and exam preparation.
The Use of Coordinates chapter introduces the Cartesian coordinate system and explains the x-axis, y-axis, origin, quadrants, and ordered pairs. Students also learn to plot and identify points, reflection of points, distance between two points, midpoint formula, section formula, and collinearity of points. These concepts help build a strong foundation for coordinate geometry.
1.0Download CBSE Notes Class 9 Maths Chapter 1 - Orienting Yourself: The Use of Coordinates Notes
These CBSE Class 9 Maths Chapter 1 notes provide a quick way to revise the use of coordinates. Students can use the notes to understand the Cartesian plane, locate points, revise important formulas, and practise coordinate-based questions.
2.0Important Concepts Class 9 Maths Chapter 1 The Use of Coordinates CBSE Notes
Cartesian Coordinate System
A Cartesian coordinate system is formed by two mutually perpendicular number lines. The horizontal line is called the x-axis, while the vertical line is called the y-axis. Their point of intersection is called the origin, represented by O. The coordinate of the origin is (0, 0).
Ordered Pair
The position of a point is written as an ordered pair (x, y). The first number gives the x-coordinate and the second number gives the y-coordinate. The order is important, so (x, y) and (y, x) are generally different points.
Abscissa and Ordinate
The x-coordinate is called the abscissa, and the y-coordinate is called the ordinate. For a point P(a, b), a is the abscissa and b is the ordinate.
Quadrants and Signs
The x-axis and y-axis divide the coordinate plane into four quadrants.
For example, (4, 5) lies in the first quadrant, while (–3, –1) lies in the third quadrant.
Points on the Axes
A point on the x-axis always has its y-coordinate as zero, so it is written as (x, 0). A point on the y-axis always has its x-coordinate as zero, so it is written as (0, y). The origin is (0, 0).
Plotting Points
To plot a point P(a, b), start from the origin. Move |a| units along the x-axis according to the sign of a. Then move |b| units upward or downward according to the sign of b. The final position gives the required point. The scale on the axes should be uniform and the numbering should begin from the origin.
Reflection of Points
Reflection gives the mirror image of a figure with respect to an axis. When a figure is reflected in the x-axis, its x-coordinate remains the same. When it is reflected in the y-axis, its y-coordinate remains the same.
Distance Formula
The distance between two points (x₁, y₁) and (x₂, y₂) is:
PQ = √[(x₂ − x₁)² + (y₂ − y₁)²]
The distance of a point (x, y) from the origin is:
√(x² + y²)
Section and Midpoint Formula
The section formula is used to find the coordinates of a point that divides a line segment in a given ratio.
The midpoint of the line segment joining (x₁, y₁) and (x₂, y₂) is:
((x₁ + x₂)/2, (y₁ + y₂)/2)
The midpoint divides a line segment in the ratio 1 : 1.
Collinearity and Geometrical Figures
Three points are collinear when they lie on the same straight line. This can be checked by comparing the lengths of the line segments. Coordinates can also be used to check properties of triangles, squares, rectangles, rhombuses, and parallelograms.
3.0Other Study Materials for Class 9 Maths
Students can use additional study materials along with these notes, such as:
4.0Why CBSE Notes Class 9 Maths - The Use of Coordinates
CBSE Class 9 Maths notes make it easier to revise The Use of Coordinates. Students can use them to go through the main topics and important points before tests and exams.
- Quick revision: Go through the chapter in less time.
- Simple learning: Understand coordinates, axes, origin, and quadrants.
- Main topics: Revise plotting points, reflection, distance, midpoint, and section formula.
- Practice: Solve textbook questions along with the notes.
- Exam revision: Read the important topics before a test or exam.
- Avoid mistakes: Learn where to write the x-coordinate and y-coordinate and how to use their signs.
- More confidence: Regular practice helps you solve coordinate questions with ease.