Cartesian Coordinate Plane

Definition

The Cartesian coordinate plane is a two-axis system for representing points as ordered pairs $(x,y)$ .

It bridges the gap between geometry and algebra, allowing spatial relationships to be manipulated through precise mathematical equations.

Axes: The horizontal x-axis and vertical y-axis intersect at the Origin (0,0).
- How to read: “The origin zero comma zero.”
- Meaning: The origin—reference point where both coordinates are zero; center of the plane.
Coordinates: Points are represented as ordered pairs $(x,y)$ , where $x$ is the horizontal distance (left/right) and $y$ is the vertical distance (up/down).
- How to read: “The ordered pair x comma y.”
- Meaning: Ordered pair— $x$ is horizontal displacement, $y$ is vertical; order matters: $(3, -2)$ is not the same as $(-2, 3)$ .
Quadrants: The axes divide the plane into four regions, numbered counterclockwise with Roman numerals:
- Quadrant I: Positive $x$ , Positive $y$ $(+, +)$
- Quadrant II: Negative $x$ , Positive $y$ $(-, +)$
- Quadrant III: Negative $x$ , Negative $y$ $(-, -)$
- Quadrant IV: Positive $x$ , Negative $y$ $(+, -)$
- How to read: “Quadrant one is plus comma plus, Quadrant two is minus comma plus, Quadrant three is minus comma minus, and Quadrant four is plus comma minus.”
- Meaning / when to use: Sign of $x$ and $y$ tells you which quadrant—and therefore the sign of trig functions at that angle.