CBSE Notes Class 9 Maths Chapter 3 Coordinate Geometry

One of the most basic topics covered in CBSE Class 9 Maths is Coordinate Geometry. This chapter serves as the basis for comprehending the geometry of shapes and how coordinates are used to place them on a two-dimensional plane. The ideas discussed here are found in the third chapter of the textbook, which covers the cartesian system, coordinate notions, plotting points, and measuring distances between points. With definitions, formulae, and solved examples, these lecture notes are made to make studying these ideas as simple as possible so that students can grasp the concept properly and be prepared for the tests.

1.0CBSE Class 9 Maths Notes Chapter-3 Coordinate Geometry - Revision

Important Concepts in Coordinate Geometry

Cartesian Plane: A two-dimensional plane divided into four quadrants by the x-axis (horizontal) and y-axis (vertical).

Coordinates of a Point: Each point on the plane is represented as an ordered pair (𝑥, 𝑦), where "𝑥" is the horizontal distance & "𝑦" is the vertical distance from the origin.

Quadrants: The Cartesian plane is divided into 4 quadrants:

• Quadrant I: Both 𝑥 and 𝑦 are positive.
• Quadrant II: 𝑥 is negative, and 𝑦 is positive.
• Quadrant III: Both 𝑥 and 𝑦 are negative.
• Quadrant IV: 𝑥 is positive, and 𝑦 is negative.

Distance Between Two Points: The distance between any 2 points (x₁, y₁) and (x₂, y₂) may be calculated using a formula.

Definitions

• Cartesian Plane: A two-dimensional plane defined by two perpendicular axes—the x-axis and the y-axis—that intersect at the origin (0, 0).
• Origin: The point of intersection of the x-axis & y-axis, denoted as (0, 0).
• Abscissa: The x-coordinate of a point, which is the horizontal distance from the origin.
• Ordinate: The y-coordinate of a point, which is the vertical distance from the origin.
• Collinear Points: Points that lie on the same straight line.

Formulas

Distance Formula:

$D=\sqrt{}\left({\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2\right)$

Midpoint Formula:

$M=\left(\left(x_1+x_2\right)/2,\left(y_1+y_2\right)/2\right)$

Section Formula (Internal Division):

$P(x,y)=\left(m{x}_2+n{x}_{1}m+n,m{y}_2+n{y}_{1}m+n\right)(mx2+nx1m+n,my2+ny1m+n)$

2.0Solved Examples 

Problem 1: Write the coordinates of the vertices of a rectangle whose length and breadth are 5 and 3 units, respectively; one vertex at the origin, the longer side lies on the x-axis, and one of the vertices lies in the third quadrant.

Solution: According to the question, the longer side means the length is the x-axis, which is 5. 

one vertex is on the origin, then its coordinates are (0,0)

Another vertex is in the third quadrant, meaning x and y both will be negative (-5, -3) 

For the other two vertices they both will be (0,3) and (5,0). 

Problem 2: Without plotting the points, indicate the quadrant in which they will lie if 

(i) ordinate is 7 and abscissa is – 2 

(ii) abscissa is – 4 and ordinate is – 6

(iii) abscissa is – 3 and ordinate is 3 

(iv) ordinate is 4 and abscissa is 9

Solution: (i) (– , +) = IInd Quadrant 

(ii) (– , – ) = IIIrd Quadrant 

(iii) (– , +) = IInd Quadrant 

(iv) (+, +) = Ist Quadrant 

Problem 3: Write whether the following statements are True or False. Justify your answer. 

(i) Point (0, –2) lies on the y-axis. 

Solution: True, whenever a point lies on the y-axis, the x-axis will always be zero like in the given coordinates. 

(ii) The perpendicular distance of the point (4, 3) from the x-axis is 4.

Solution: False, the perpendicular distance means the vertical distance from the given point or line hence, the perpendicular distance from the x-axis is 3 not 4. 

Problem 4: Three vertices of a rectangle are (5, 2), (– 3, 2) and (– 3, –5). Plot these points and find the coordinates of the fourth vertex.

Solution: 

As the given vertices are of a rectangle hence, the opposite edges of the rectangle will be equal, meaning the fourth coordinate will be (5, –5).

3.0Tips and Tricks

• Remembering Quadrants: Start from the top-right quadrant (Quadrant I) and move counterclockwise.
• Shortcut for Distance Formula: Visualise the points as vertices of a right triangle; use the Pythagorean theorem for quicker calculations.
• Practice Plotting Points: Familiarise yourself with the Cartesian plane by practising the plotting of points in different quadrants.
• Use Visual Aids: Draw diagrams to simplify distance and midpoint problems.

4.0Key Features of CBSE Class 9 Maths Notes Chapter 3 Coordinate Geometry

Comprehensive Explanations: These notes break the rigid sections of problems like the Cartesian system, distance formula, and section formula into easy, into simple concepts for easy grasp.

Easy-to-Understand Language: Even the most complicated concepts would appear simple to the students because of the simple language used.

Graphical Illustrations: Include graphs of plotted points and line segments, showing distances and midpoints visually.

Practice Problems: There are a lot of practice questions that can help the student retain the information and apply it. This improves accuracy and confidence.

Revision-Friendly Format: The notes have finally found their ideal use in quick revision before exams, as this tends to save time and effort because it summarises the key points of the session.

These features guarantee that the CBSE Class 9 Maths Notes for Chapter 3 on Coordinate Geometry are a thorough resource for understanding the topic, not merely a study help.