A four quadrants graph is the standard coordinate plane you meet in maths class. Two number lines cross at right angles and split the page into four regions, which makes it easy to plot points and read positions.
How the plane is built
The horizontal line is the x-axis and the vertical line is the y-axis. They meet at the origin, written (0, 0). Every point is described by an ordered pair (x, y): move left or right first, then up or down.
The four quadrants
| Quadrant | Sign of x | Sign of y | Example |
|---|---|---|---|
| I (top right) | + | + | (3, 4) |
| II (top left) | − | + | (−3, 4) |
| III (bottom left) | − | − | (−3, −4) |
| IV (bottom right) | + | − | (3, −4) |
The numbering runs anticlockwise, starting at the top right. Points that sit exactly on an axis do not belong to any quadrant.
How to plot a point
- Start at the origin.
- Move along the x-axis by the first number: right if positive, left if negative.
- From there, move along the y-axis by the second number: up if positive, down if negative.
- Mark the spot and label it.
To plot (−2, 5), go two units left and five units up. You land in quadrant II.
Where it is used
Four quadrant graphs turn up in algebra for drawing lines and curves, in geometry for reflecting and rotating shapes, and in science for data that can go negative, such as temperature changes or profit and loss. A handy habit is to check the signs first: they tell you the quadrant before you draw anything, which is a quick way to catch a mistake.
A tip for students: when you check homework, glance at every answer and ask whether the signs make sense for the quadrant. Sketching a rough graph in the margin takes ten seconds and catches most sign errors before a teacher does.
Quick questions
What is the origin?
It is the point (0, 0), where the x-axis and y-axis cross.
Which quadrant is (0, 5) in?
None. A point on an axis does not belong to a quadrant.
Why do we number the quadrants anticlockwise?
It is a mathematical convention that matches the way angles are measured, starting from the positive x-axis.
Key takeaways about four quadrants graph
Here is a short summary of four quadrants graph so you can find the main points quickly.
- A four quadrants graph is the standard coordinate plane you meet in maths class.
- The horizontal line is the x-axis and the vertical line is the y-axis.
- The numbering runs anticlockwise, starting at the top right.
- To plot (−2, 5), go two units left and five units up.
- Four quadrant graphs turn up in algebra for drawing lines and curves, in geometry for reflecting and rotating shapes, and in science for data that can go negative, such as temperature changes or profit and loss.
- A tip for students: when you check homework, glance at every answer and ask whether the signs make sense for the quadrant.
- It is the point (0, 0), where the x-axis and y-axis cross.
- It is a mathematical convention that matches the way angles are measured, starting from the positive x-axis.
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Related reading:
For general background, you can look up four quadrants graph on Wikipedia.
