Coordinate Geometry Class 9 Notes CBSE Maths Chapter 3 (Free PDF Download)

Coordinate geometry is a subject of mathematics that bridges the gap between algebra and geometry.

With the use of algebra, we describe a variety of geometrical relationships.

Coordinate Axes:

• Coordinate axes are formed when two perpendicular lines, \[\text{XOX }\!\!'\!\!\text{ }\] and \[\text{YOY }\!\!'\!\!\text{ }\] , connect at the point \[\text{O}\].

• The origin that is point \[\text{O}\] is the starting point for measuring distances.

• The plane is divided into four quadrants by the axes, numbered as \[\text{I, II , III}\] and \[\text{IV}\].

• The plane is known as the Cartesian plane, coordinate plane, or \[\text{XY}\] - plane.

• The Cartesian plane is the plane that contains the axes.

• The lines \[\text{XOX }\!\!'\!\!\text{ }\] and \[\text{YOY }\!\!'\!\!\text{ }\] are known as the \[\text{x}\] -axis and \[\text{y}\] -axis, respectively, and are normally drawn horizontally and vertically.

• The origin is defined as the point \[\text{O}\] where two axes connect.

• Abscissae are the values of \[\text{x}\] measured along the \[\text{x}\] - axis from \[\text{O}\]. 

• As seen in the image, the values of \[\text{x}\] are positive along \[\text{OX}\] and negative along \[\text{OX }\!\!'\!\!\text{ }\].

• Similarly, the values of \[\text{y}\] are called ordinates because they are measured from \[\text{O}\] along the \[\text{y}\] - axis.

• As seen in the picture, the values of  \[\text{y}\] are positive along \[\text{OY}\] and negative along \[\text{OY }\!\!'\!\!\text{ }\].

• When we express a point's abscissa and ordinate as (abscissa, ordinate), we get its coordinates.

Example:

If a point's abscissa is $6$ and its ordinate is $2$ ,the point’s coordinates are expressed as $\left( 6,2 \right)$.

• Assume that \[\text{A}\] is a point on the plane. \[\text{AC}\bot \text{XOX }\!\!'\!\!\text{ }\] and \[\text{AB}\bot \text{YOY }\!\!'\!\!\text{ }\]should be drawn.

• The ordered pair \[\left( \text{x,y} \right)\] is said to define the point \[\text{A}\] if \[\text{OC=x}\] and \[\text{OB=y}\].

• \[\text{A}\]'s Cartesian coordinates are also known as \[\text{x}\] and \[\text{y}\].

• As a result, we can associate an ordered pair \[\left( \text{x,y} \right)\] of real numbers with each point in the plane.

• We can, on the other hand, map a point in the plane given an ordered pair of numbers.

• If $\text{x}\ne \text{y}$, then the location of $\left( \text{x,y} \right)$ in the Cartesian plane differs from the position of $\left( \text{y,x} \right)$.

• As a result, if we swap the $\text{x}$ and $\text{y}$ coordinates, the position of  $\left( \text{y,x} \right)$will be different from that of $\left( \text{x,y} \right)$. This indicates that the sequence in which $\text{x}$ and $\text{y}$ appear is crucial $\left( \text{x,y} \right)$.

• $\left( \text{x,y} \right)$ is referred to as an ordered pair.

• The ordered pair  $\left( \text{x,y} \right)\ne $ ordered pair $\left( \text{y,x} \right)$.

Coordinate Geometry Class 9 Notes – A Short Synopsis

We provide the students with the option of Class 9 Maths Chapter 3 PDF download. This makes it feasible for the students to revise the syllabus easily in an offline format. Moreover, it eliminates the hassle of surfing the web every time the students plan on studying. Students can download the Chapter 3 Maths Class 9 Notes through the Vedantu website, and get their studies going easily. It is also a good option for students during their group studies.

Notes of Coordinate Geometry: Topics Covered

The notes of Class 9 Maths Chapter 3 cover the following topics:

• Cartesian System and the terms along with it

• Coordinate geometry and its definition

• Relationship between the signs of the coordinates of a given point, further describing the quadrant in which the point lies

• Locating the point in the plane when the coordinates of the point are given

• Plotting of the points in the cartesian plane

Class 9 Coordinate Geometry Notes

Cartesian System

Cartesian Plane

It is defined as two number lines that are perpendicular to each other, known as the x-axis and y-axis. The horizontal line is called the x-axis and the vertical line is called the y-axis. These lines combined together are called the coordinate axes. Further, the cartesian plane can be extended infinitely towards all directions.

Origin:

The point at which both the axes intersect perpendicularly is called the origin. The intersection of these axes takes place at right angles.

Quadrants:

The cartesian plane above mentioned is divided into four parts, namely, quadrants. The quadrants are named I, II, III and IV and are in the anti-clockwise order. It starts with the upper right corner.

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Signs of Points In Different Coordinates in The Cartesian Plane

The signs of the points placed in different quadrants across a cartesian plane are as follows:

1. Quadrant: x-coordinate is positive and y-coordinate is positive. For e.g., (+2,+3)

2. Quadrant: x-coordinate is negative and y-coordinate is positive. For e.g., (-2,+3)

3. Quadrant: x-coordinate is negative and y-coordinate is negative. For e.g., (-2,-3)

4. Quadrant: x-coordinate is positive and y-coordinate is negative. For e.g., (+2,-3)

Plotting of Points on a Graph

The plotting of points on a given graph can be done easily in the plane with an ordered number of pairs by using the coordinate axes. If a point A is given with the coordinates (x,y), then, x is the abscissa and y is the ordinate.

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How to Plot A Point on The Cartesian Plane? 

The location of a point in the cartesian plane is defined using the coordinate points. The x-point represents the point at which it lies on the horizontal axis, while the y-point represents the point at which it lies on the vertical axis.

Consider the point (-1,-2). This point is 1 unit away from the negative x-axis and similarly, -2 is 2 units away from the negative y-axis. The other points can be easily plotted in a similar manner. 

While plotting the points, the students need to take special note of the unit they are following for the respective axes and they must then plot the points accordingly. 

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Notes of Coordinate Geometry Class 9 - How Will they Help?

The Class 9 Mathematics test is worth 80 points. Coordinate geometry receives 6 points out of this total. This chapter is usually about 2-3 questions. Based on the mark distribution, they might be short or extensive replies. This chapter is simple and easy to finish. As a result, it is prudent for pupils to grasp and comprehend its principles thoroughly. This will help them receive full credit for this chapter.

Moreover, the additional point is that this chapter is interesting because the students can learn the concepts easily using a practical approach. You can always check the notes that we provide. They comprehensively cover all the key topics and questions involved in the chapter. This further makes the learning and revision process easier.

Why Choose Vedantu Class 9 Coordinate Geometry Notes?

Here are some of the key reasons why you must choose Vedantu notes:

• These notes are designed to inculcate the right attitude of study towards the students. 

• It allows the students to clarify the fundamentals of the chapter.

• The notes help students to identify the important pointers to learn for the exams.

• Referring to the revision notes helps students to organise their learning.

• Once students download the PDF, they can revise the important formulas and concepts of the chapter anytime and from anywhere.

Important Question for Practice

1. Find minimum 3 solutions for the following linear equations in two variables:

2x - 3y = -11.

2. Find 4 solutions for the equation 12x + 5y = 0.

3. Plot the following points and determine whether they are collinear or not:

(1, 3), (– 1, – 1), (– 2, – 3)

4. Points P (5, 3), Q (–2, 3), and S (5, –4) are three vertices of a square PQRS. Plot these points on a graph paper and hence find the coordinates of the vertex R.

5. Locate the following points in the cartesian plane:

(5, 0), (0, 5), (2, 5), (5, 2), (–3, 5), (–3, –5), (5, –3), and (6, 1).

Conclusion

Coordinate Geometry is perhaps one of the more straightforward topics in the Class 9 curriculum. We use a step-by-step approach to the solutions to help students comprehend the ideas and be more interested in studying. Diagrams are supplied alongside for a better understanding of the concepts. We make certain that pupils get the knowledge promptly. These notes aid pupils in their preparation for Class 9 Mathematics and other competitive examinations. We suggest students to review the concepts on a frequent basis in order to remove their concerns and do better in the exams. Our specialists create these notes to assist students in achieving high scores in Class 9 Mathematics.