# Definition:Cartesian Plane/Quadrants

## Definition

For ease of reference, the cartesian plane is often divided into four quadrants by the axes:

### First Quadrant

Quadrant $\text{I}: \quad$ The area above the $x$-axis and to the right of the $y$-axis is called **the first quadrant**.

That is, **the first quadrant** is where both the $x$ coordinate and the $y$ coordinate of a point are positive.

### Second Quadrant

Quadrant $\text{II}: \quad$ The area above the $x$-axis and to the left of the $y$-axis is called **the second quadrant**.

That is, **the second quadrant** is where the $x$ coordinate of a point is negative and the $y$ coordinate of a point is positive.

### Third Quadrant

Quadrant $\text{III}: \quad$ The area below the $x$-axis and to the left of the $y$-axis is called **the third quadrant**.

That is, **the third quadrant** is where both the $x$ coordinate and the $y$ coordinate of a point are negative.

### Fourth Quadrant

Quadrant $\text{IV}: \quad$ The area below the $x$-axis and to the right of the $y$-axis is called **the fourth quadrant**.

That is, **the fourth quadrant** is where the $x$ coordinate of a point is positive and the $y$ coordinate of a point is negative.

Note that the axes themselves are generally not considered to belong to any quadrant.

## Sources

- 1968: Murray R. Spiegel:
*Mathematical Handbook of Formulas and Tables*... (previous) ... (next): $\S 5$: Trigonometric Functions - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**Cartesian coordinate system** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**Cartesian coordinate system**