Mind Map:: Chapter 3:: Coordinate Geometry

Class IX Mathematics - Chapter 3: Coordinate Geometry

Coordinate Geometry

Coordinate geometry is the study of geometry using a coordinate system. The plane is divided by two perpendicular lines, the x-axis (horizontal) and y-axis (vertical), forming the coordinate plane.

Important Points:

• The plane is divided into four quadrants by the coordinate axes.
• The point of intersection of the axes is called the origin.

Example:

The coordinates of a point (x, y) in the plane are determined by its distance from the x-axis and y-axis.

Coordinate Axes

The coordinate axes consist of the x-axis (horizontal) and y-axis (vertical). They divide the plane into four quadrants.

Important Points:

• The x-axis is horizontal, and the y-axis is vertical.
• The point of intersection of the axes is called the origin.

Example:

The coordinates of the origin are (0, 0).

Quadrants

The coordinate plane is divided into four quadrants:

Important Points:

• First quadrant: (+, +)
• Second quadrant: (–, +)
• Third quadrant: (–, –)
• Fourth quadrant: (+, –)

Example:

If the coordinates of a point are (3, 4), it lies in the first quadrant, as both coordinates are positive.

Coordinates

Coordinates are the ordered pair (x, y) that represent a point in the coordinate plane.

Important Points:

• The first value (x) is called the abscissa (distance from the y-axis).
• The second value (y) is called the ordinate (distance from the x-axis).

Example:

The coordinates (2, 3) represent a point 2 units to the right of the y-axis and 3 units above the x-axis.

x- and y-Coordinates

The coordinates of a point can be represented as (x, 0) on the x-axis or (0, y) on the y-axis.

Important Points:

• Points on the x-axis have coordinates of the form (x, 0).
• Points on the y-axis have coordinates of the form (0, y).

Example:

A point on the x-axis, such as (4, 0), has no y-coordinate, while a point on the y-axis, such as (0, 5), has no x-coordinate.

Point Equality

Two points are equal if their x- and y-coordinates are equal.

Important Points:

• If \( x \neq y \), then \( (x, y) \neq (y, x) \).
• If \( x = y \), then \( (x, y) = (y, x) \).

Example:

For the points \( (2, 3) \) and \( (3, 2) \), \( (2, 3) \neq (3, 2) \), as their coordinates are not equal.