The Cartesian coordinate system uses two perpendicular number lines to fix the position of any point on a plane. The horizontal line is the x-axis and the vertical line is the y-axis. They cross at the origin, whose coordinates are (0, 0).
Reading a point
Every point is written as an ordered pair (x, y). The first number, x, tells how far left or right of the origin the point is. The second number, y, tells how far up or down. Order matters: (3, 2) is not the same point as (2, 3).
Worked example
A point is 3 units to the right of the origin and 2 units up. Its coordinates are (3, 2). A point 4 units left and 1 unit down would be (−4, −1).
The four quadrants
The two axes split the plane into four quadrants, numbered anticlockwise from the top right.
Key idea
| Quadrant I | (+, +) |
| Quadrant II | (−, +) |
| Quadrant III | (−, −) |
| Quadrant IV | (+, −) |
Remember
- A point on the x-axis has y = 0, e.g. (3, 0).
- A point on the y-axis has x = 0, e.g. (0, −5).
- Always write coordinates as (x, y) — x first, then y.