Understanding Cartesian Coordinates

What Are Cartesian Coordinates?

Cartesian coordinates are a way of representing points in a plane using two numbers, usually denoted as (x, y). These numbers indicate the position of a point relative to two perpendicular lines called axes.

For example:

• The point (3, 2) is 3 units along the x-axis and 2 units along the y-axis.

The Cartesian Plane

• X-axis: The horizontal line where y = 0.
• Y-axis: The vertical line where x = 0.
• Origin: The point (0, 0) where the x-axis and y-axis intersect.

Quadrants of the Cartesian Plane

The Cartesian plane is divided into four quadrants:

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

Plotting Points

1. Identify the x-coordinate: Move horizontally from the origin.
2. Identify the y-coordinate: Move vertically from the x-coordinate.
3. Mark the point: Where these two movements intersect is the location of the point.

Examples

Example 1: Plot the Point (4, -3)

Example 2: Plot the Point (-2, 5)