### Learning Objectives

- Identify Quadrants on the Coordinate Plane
- Identify the four quadrants of a coordinate plane
- Given an ordered pair, determine its quadrant

## Identify quadrants and use them to plot points

The intersecting *x-* and *y-*axes of the coordinate plane divide it into four sections. These four sections are called **quadrants**. Quadrants are named using the Roman numerals I, II, III, and IV beginning with the top right quadrant and moving counter clockwise.

Ordered pairs within any particular quadrant share certain characteristics. Look at each quadrant in the graph below. What do you notice about the signs of the *x-* and *y-*coordinates of the points within each quadrant?

Within each quadrant, the signs of the *x-*coordinates and *y-*coordinates of each ordered pair are the same. They also follow a pattern, which is outlined in the table below.

Quadrant | General Form of Point in this Quadrant | Example | Description |
---|---|---|---|

I | [latex](+,+)[/latex] | [latex](5,4)[/latex] | Starting from the origin, go along the x-axis in a positive direction (right) and along the y-axis in a positive direction (up). |

II | [latex](−,+)[/latex] | [latex](−5,4)[/latex] | Starting from the origin, go along the x-axis in a negative direction (left) and along the y-axis in a positive direction (up). |

III | [latex](−,−)[/latex] | [latex](−5,−4)[/latex] | Starting from the origin, go along the x-axis in a negative direction (left) and along the y-axis in a negative direction (down). |

IV | [latex](+,−)[/latex] | [latex](5,−4)[/latex] | Starting from the origin, go along the x-axis in a positive direction (right) and along the y-axis in a negative direction (down). |

Once you know about the quadrants in the coordinate plane, you can determine the quadrant of an ordered pair without even graphing it by looking at the chart above. Here’s another way to think about it.

The example below details how to determine the quadrant location of a point just by thinking about the signs of its coordinates. Thinking about the quadrant location before plotting a point can help you prevent a mistake. It is also useful knowledge for checking that you have plotted a point correctly.

### Example

In which quadrant is the point [latex](−7,10)[/latex] located?

### Example

In which quadrant is the point [latex](−10,−5)[/latex] located?

What happens if an ordered pair has an *x*– or *y-*coordinate of zero? The example below shows the graph of the ordered pair [latex](0,4)[/latex].

A point located on one of the axes is not considered to be in a quadrant. It is simply on one of the axes. Whenever the *x-*coordinate is 0, the point is located on the *y-*axis. Similarly, any point that has a *y-*coordinate of 0 will be located on the *x-*axis.

Here are more examples of determining Quadrants:

## Summary

The coordinate plane is a system for graphing and describing points and lines. The coordinate plane is comprised of a horizontal (*x*-) axis and a vertical (*y-*) axis. The intersection of these lines creates the origin, which is the point [latex](0,0)[/latex]. The coordinate plane is split into four quadrants. Together, these features of the coordinate system allow for the graphical representation and communication about points, lines, and other algebraic concepts.