Quadrants and Coordinates

The coordinate plane (also known as the Cartesian plane or xy-plane) is divided into four regions by the x-axis (the horizontal line) and the y-axis (the vertical line). These four regions are called quadrants.

The following diagram shows the four quadrants of the Cartesian or coordinate plane. Scroll down the page for more examples and solutions.

 

Coordinate Geometry Worksheets
Practice your skills with the following worksheets:
Printable & Online Coordinate Geometry Worksheets

Understanding the Axes and the Origin:

• The x-axis goes horizontally. Values to the right of the point where the axes cross (the origin) are positive, and values to the left are negative.
• The y-axis goes vertically. Values above the origin are positive, and values below are negative.
• The origin is the point where the x-axis and y-axis intersect. Its coordinates are (0, 0). The origin does not belong to any quadrant.

The Four Quadrants:
The quadrants are numbered using Roman numerals in a counter-clockwise direction, starting from the top right:
Quadrant I (Q1):
Located in the top right of the coordinate plane.
Both the x-coordinate and the y-coordinate of any point in this quadrant are positive (+, +).
Quadrant II (Q2):
Located in the top left of the coordinate plane.
The x-coordinate of any point in this quadrant is negative, and the y-coordinate is positive (-, +).
Quadrant III (Q3):
Located in the bottom left of the coordinate plane.
Both the x-coordinate and the y-coordinate of any point in this quadrant are negative (-, -).
Quadrant IV (Q4):
Located in the bottom right of the coordinate plane.
The x-coordinate of any point in this quadrant is positive, and the y-coordinate is negative (+, -).

Coordinates:
A point on the coordinate plane is represented by an ordered pair of numbers (x, y), where:
x is the x-coordinate (also called the abscissa), representing the horizontal distance of the point from the y-axis.
y is the y-coordinate (also called the ordinate), representing the vertical distance of the point from the x-axis.

Graphing Points & Identifying Quadrants on the Coordinate Plane
This video looks at graphing ordered pairs on the coordinate plane, identifying quadrants, and providing ordered pairs for points located on the coordinate plane. It includes 10 examples.

• Show Video

Try out our new and fun Fraction Concoction Game.

Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.