Coordinates and distances on a plane
Orthonormal reference frame and coordinates of a point
What is a coordinate system?
A coordinate system in the plane is defined by an origin O and two non-parallel axes, each marked with a unit. It is denoted by (O; I, J). When the two axes are perpendicular and graduated in the same unit, the coordinate system is said to be orthonormal: this is the coordinate system most commonly used in secondary school.
Co-ordinates of a point
Every point M in the plane is identified by a pair (x; y) called the co-ordinates of M: x is the x-co-ordinate (horizontal position), y is the y-co-ordinate (vertical position).
Example: A(3; -2) means that A lies 3 units to the right of the y-axis and 2 units below the x-axis.
Reading a table of coordinates
| Point | x-coordinate | y-coordinate |
|---|---|---|
| A | 3 | -2 |
| B | -1 | 4 |
| C | 0 | 5 |
Point C has an x-coordinate of zero: it therefore lies on the y-axis. Similarly, a point with a y-coordinate of zero (y=0) lies on the x-axis.
Pitfalls to avoid
- Never reverse the order: we always write (x-coordinate; y-coordinate), never the other way round.
- The pair (2; 5) and the pair (5; 2) represent two different points.
- The origin of the coordinate system always has coordinates (0; 0).