## The coordinate plane

A coordinate plane is a two-dimensional surface divided into four quadrants by the x- and y-axes. The x-axis is the horizontal axis, and the y-axis is the vertical axis. The four quadrants are labelled as follows:

### The x-axis

The x-axis is the horizontal line that runs from left to right across the coordinate plane. It is also sometimes called the “real axis” or the “linear axis”. The x-axis is used to locate points on a graph by their x-coordinates. The x-axis is divided into quadrants, numbered from left to right, as shown in the diagram below.

The y-axis is the vertical line that runs from top to bottom across the coordinate plane. It is also sometimes called the “imaginary axis” or the “imaginary line”. The y-axis is used to locate points on a graph by their y-coordinates. The y-axis is divided into quadrants, numbered from top to bottom, as shown in the diagram below.

The point where the x- and y-axes intersect is called the origin. The coordinates of the origin are (0, 0).

### The y-axis

The y-axis is the vertical axis on a graph. The coordinate plane has four quadrants, each represented by a Roman numeral. The Quadrant I is in the upper right hand corner and contains positive x-values and y-values. The Quadrant II is in the upper left hand corner and contains negative x-values and positive y-values. The Quadrant III is in the lower left hand corner and contains negative x-values and y-values. The Quadrant IV is in the lower right hand corner and contains positive x-values and negative y-values. The point (0,0) is where the x and y axes intersect, and it is considered to be in Quadrant I.

## Quadrants

There are four quadrants in a coordinate plane. They are numbered as 1, 2, 3, and 4. Quadrant 1 is the upper right quadrant. It contains all points with positive x-coordinates and positive y-coordinates. Quadrant 2 is the upper left quadrant. It contains all points with negative x-coordinates and positive y-coordinates. Quadrant 3 is the lower left quadrant. It contains all points with negative x-coordinates and negative y-coordinates. Quadrant 4 is the lower right quadrant. It contains all points with positive x-coordinates and negative y-coordinates.

### Quadrant I

The four quadrants of a coordinate plane are often referred to as “quadrant I,” “quadrant II,” “quadrant III,” and “quadrant IV.” Each quadrant contains one-fourth of the plane. In other words, if you divide the coordinate plane into four equal sections, each section will be a quadrant.

Quadrant I is the upper right quadrant. It is sometimes referred to as the “positive” quadrant because both the x-coordinates and the y-coordinates are positive in this quadrant. All points in Quadrant I satisfy the following inequalities:

x > 0 and y > 0

### Quadrant II

Quadrant II is the upper right quadrant of a coordinate plane and contains positive values for both the x-axis and y-axis. This quadrant is also sometimes referred to as the “first quadrant” because it’s the first one you encounter when reading or moving around a coordinate plane in a clockwise direction.

### Quadrant III

Quadrant III is the quadrant of the Cartesian coordinate plane that contains the points with positive (x) coordinates and negative (y) coordinates. It is also sometimes referred to as the third quadrant or the upper right quadrant.

### Quadrant IV

In Quadrant IV, which is also sometimes known as the “final quadrant,” the angle is between 90 and 180 degrees. This quadrant is also sometimes referred to as the “danger zone” because it is where most accidents occur.

## Degrees

There are four quadrants in a coordinate plane. The four quadrants are numbered as follows. Q1 is in the upper right-hand corner. Q2 is in the upper left-hand corner. Q3 is in the lower left-hand corner. Q4 is in the lower right-hand corner. To find out what quadrant a certain angle is in, we need to know what direction it is pointing.

### 0 degrees

The angle 0° is located at the center of a protractor, so it is considered a neutral angle. It is sometimes rounded to the nearest whole number, which would be 0. When an angle is given without any specified quadrant, it is assumed to be in quadrant I or IV. So, an angle of 30° could either be in quadrant I or II; 45° could either be in quadrant I or IV; 90° must be in quadrant I, and so on.

### 45 degrees

45 degrees is in the first quadrant.

### 90 degrees

90 degrees is in the fourth quadrant.

### 135 degrees

135 degrees is in the second quadrant.

### 180 degrees

180 degrees, also known as a “straight line”, is the angle between two perpendicular lines. It is also the angle between two perpendicular planes, such as a wall and the floor.

### 225 degrees

225 degrees is in the 3rd quadrant.

### 270 degrees

270 degrees is in the third quadrant.

### 315 degrees

315 degrees is in the third quadrant.