Coordinate Geometry Class 9

We already know how to locate the points on the number line. We even know how to tell the position of the point on the number line. In this article on the coordinate geometry of class 9, we will discuss the cartesian system where we will learn how to place a point in the Cartesian system and how to plot a point in a plane when the coordinates are given.

Coordinate Geometry Class 9-

Here we will first start with the discussion of the Cartesian system. We are already aware of a number line and how to position the points on the number line. On the number line, distances from a fixed point are marked in equal units positively in one direction and negatively in the other direction. The point from where these distances are marked is called the origin. A number line is used to represent the numbers by marking points on a line at equal distances. If we move 1 unit then it represents the number ‘1’ and if we move four units from the origin, it is called ‘4’ units. ‘0’ is the origin. The point in the positive direction at a distance r from the origin represents the number ‘r’. The point in the negative direction at a distance r from the origin represents the number ‘- r’. 

Descartes gave the idea of placing two such lines perpendicular to each other on a plane and locating the points on the plane by referring them to these lines. The perpendicular line can be in any direction. 

But when we are choosing these two lines to locate a point in the plane. Here, one line will be vertical and the other will be horizontal. 

Coordinate Geometry Class 9 Full Chapter Explanation

Let us understand the cartesian system. Take two number lines, let them be X’X and Y’Y. Place the X’X horizontally and number them as we do in a number line. Likewise, do the same thing with Y’Y and place them vertically. Combine both the lines in such a way that the two lines cross each other at their zero (also called origin). 

Here, the horizontal line X’X is called the x-axis, and the vertical line Y’Y is called the y-axis. The point where X’X and Y’Y cross is called the origin. It is denoted by ‘O”. The positive numbers lie in the direction of OX and OY. OX and OY are called the positive directions of the x-axis and y-axis respectively. Similarly, OX’ and OY’ are called the negative directions of the x-axis and the y-axis respectively. 

By constructing this way, we observe that both of the axes are dividing the plane into four equal parts.

These four parts are said to be quadrants numbered I, II, III, and IV quadrants counterclockwise from OX. So, the plane consists of axes and quadrants. This plane is called the Cartesian plane or xy-plane or coordinate plane. The axes are called coordinate axes. 

This system is useful, to describe the location of any point. We write the coordinate of a point using the following conventions-

• The x-coordinate of a point is its perpendicular distance from the y-axis measured along the x-axis. Positive along the positive direction of the x-axis and negative along the negative direction of the x-axis. The x-coordinate is also called the abscissa.
• The y-coordinate of a point is its perpendicular distance from the x-axis measured along the y-axis. Positive along the positive direction of the y-axis and negative along the negative direction of the y-axis. The y-coordinate is also called ordinate. 
• While stating the coordinate of a point in the coordinate plane, the x-coordinates come first and then the y-coordinate. Coordinates are represented in brackets.

For example- we say that the coordinate of any point A is (4,8).

The coordinates of the origin O are decided on its placement on a number line. Since there is zero distance from both the axes its abscissa and ordinate are both zero. Hence, the coordinate of the origin is (0, 0). 

Note- The system we have talked about above about how to describe a point in a plane is only a convention, which is accepted all over the world. 

Coordinate Chapter Class 9 Notes

The coordinate geometry class 9 notes include the topic, like 

Plotting a Point in the Plane when the coordinates are given-

Before we have discussed how to find the coordinates when the point is given. Here, we will discuss how to place the point in the plane when we already know the coordinates. This method is called ‘plotting the points’. 

Suppose the coordinate of the given point is (5, 2). You have to plot this point in the coordinate plane. We draw the coordinate axes. You have to choose the unit such that one centimeter represents one unit on both axes. The coordinate of the given point (5, 2) tells that the distance of this point from the y-axis along the positive x-axis is 5 units, and the distance of the point from the x-axis along the positive y-axis is 2 units. Starting from origin O, we count 5 units on the positive x-axis and mark the corresponding point as P. Now starting from P, we move in the positive direction of the y-axis and count 2 units and mark the corresponding point as Q. You will observe the distance of Q from the y-axis is 5 units and from the x-axis is 2 units. Hence, Q is the position of the point. Q lies in the first quadrant since both the coordinates of Q are positive. 

Conclusion

Above we have already discussed the Cartesian system, which is the universal system of denoting the point. Here we have talked in detail about how to place a point in the Cartesian system and how to plot a point in a plane when the coordinates are given. These are the primary topics of this article. In this, we have even discussed the plotting of the Cartesian plane, and how to plot.