## Revision Notes ofÂ Ch 3Â Coordinate Geometry Class 9th Math

**Topics in the Chapter**

- Cartesian plane and the terms associated with it
- Cartesian system
- Coordinate Geometry
- Relationship between the signs of the coordinates of a point and the quadrant of the point in which it lies.
- Location of the point in the plane when its coordinates are given
- Plotting a point in the Cartesian Plane

**Cartesian plane and the terms associated with it**

**Cartesian system**

A Cartesian system consists of two perpendicular lines: one of them is horizontal and the other is vertical.

The horizontal line is called the x- axis and the vertical line is called the y -axis. The point of intersection of the two lines is called origin, and is denoted by O.

â€¢ XOX' is called the x-axis; YOY' is called the y-axis; the point O is called the origin,Â

â€¢ Positive numbers lie on the directions of OX and OY.Â

â€¢ Negative numbers lie on the directions of OX' and OY'.Â

â€¢ OX and OY are respectively called positive x-axis and positive y-axis.Â

â€¢ OX' and OY are respectively called negative x-axis and negative y-axis.Â

â€¢ TheÂ axes divide the plane into four equal pans. The four parts are called quadrants,Â numbered l, II, Ill and IV, in anticlockwise from positive x-axis, OX,Â

â€¢ The plane is also called co-ordinate plane or Cartesian plane or xy-plane.Â

**Coordinate Geometry**

Example:

Name the quadrant or the axis in which the points (5, â€“4), (2, 7) and (0, â€“9) lie?

â€¢ The coordinates of the point (5, â€“4) are of the form (+, â€“). Hence, (5, â€“4) lie in quadrant IV

â€¢ The coordinates of the point (2, 7) are of the form (+, +). (2, 7) lie in quadrant I.

â€¢ The coordinates of the point (0, â€“9) are of the form (0, b). (0, â€“9) lie on the y-axis

â€¢ The coordinates of a point on the coordinate plane can be determined by the following conventions.

â€¢ The x-coordinate of a point is its perpendicular distance from the y-axis, measured along the x-axis (positive along the positive x-axis and negative along the negative x-axis). The x-coordinate is also called the abscissa.

â€¢ The y-coordinate of a point is its perpendicular distance from the x-axis, measured along the y-axis ( positive along the positive y-axis and negative along the negative y -axis). The y-coordinate is also called the ordinate.

â€¢ In stating the coordinates of a point in the coordinate plane, the x-coordinate comes first

and then the y-coordinate. The coordinates are placed in brackets.

**It is observed that**

x-coordinate of point A is 5

y-coordinate of point A is 2

Coordinates of point A are (5, 2).

x-coordinate of point C is â€“5

y-coordinate of point C is 2

Coordinates of point C are (â€“5, 2).

**Note:**The coordinates of the origin are (0, 0). Since the origin has zero distance from both

the axes, its abscissa and ordinate are both zero.

**Relationship between the signs of the coordinates of a point and the quadrant of the point in which it lies**

â€¢ The 1st quadrant is enclosed by the positive x-axis and positive y-axis. So, a point in the 1st quadrant is in the form (+, +).

â€¢ The 2nd quadrant is enclosed by the negative x-axis and positive y-axis. So, a point in the 2nd quadrant is in the form (â€“, +).

â€¢ The 3rd quadrant is enclosed by the negative x-axis and the negative y-axis. So, the point in the 3rd quadrant is in the form (â€“, â€“).

â€¢ The 4th quadrant is enclosed by the positive x-axis and the negative y-axis. So, the point in the 4th quadrant is in the form (+, â€“).

**Note:**The coordinates of the point on the x-axis are of the form (a, 0) and the coordinates

of the point on the y-axis are of the form (0, b), where a, b are real numbers.

**Plotting a point in the Cartesian Plane**

We can plot a point in the Cartesian plane, if the coordinates of the points are given.

**Example: Plot the points A (5, â€“3) and B (â€“2, 5) on the Cartesian plane.**

__To plot A (5, â€“3):__

(1) Move 5 units along OX and mark the endpoint as M.

(2) From M and perpendicular to the x-axis, move 3 units along OY'. Mark the endpoint as A.

This is the location of the point (5, â€“3) on the Cartesian plane.

This is the location of the point (5, â€“3) on the Cartesian plane.

__To plot B (â€“2, 5):__

(1) Move 2 units along OX' and mark the endpoint as N.

(2) From N and perpendicular to the x-axis, move 5 units along OY. Mark the endpoint as B.

This is the location of the point (â€“2, 5) on the Cartesian plane.

This is the location of the point (â€“2, 5) on the Cartesian plane.

â€¢ Points A and B are plotted in the following graph.