Not only the world of mathematics, but also many aspects of our daily life have to do in some way with locations in space: the location of a street, the location of our house, the theater seat. Therefore, it is important to know the way in which we can describe the position of a point in space; this is done by means of **coordinates**.

The coordinate system we use most frequently is the **Cartesian (or rectangular) system**, named in honor of the famous French philosopher and mathematician, René Descartes (1556 - 1650), who shares with the French lawyer and mathematician Pierre Fermat (1601 - 1665), the credit for his invention.

**Cartesian coordinates**

To represent the location of any point P on a plane, we rely on a coordinate system formed by two lines perpendicular to each other, which intersect in a point **zero** (Figure I).

- The lines are called
**coordinate axes**and the point of intersection**center or origin**. - The lines divide the plane into four parts, called
**quadrants**, numbered from I to IV in a counterclockwise direction. - The horizontal axis is called
**x axis or axis of the abscissa**and it has its positive part to the right of the center and its negative part to the left. - The vertical axis is called
**axis and or axis of the ordinates**and it has its positive part up and its negative part down.

**Coordinates of a point**

Any point P on the plane is specified by a pair of real numbers called **point coordinates**.** **These points are written in order, first that of the horizontal axis (called **abscissa**) and then the vertical axis (called **ordered**):

**P (abscissa, ordered)**

To obtain these coordinates of the point P (x, y), we draw a line parallel to the x axis that passes through P; the cut-off point of this line with the x-axis is at a distance **x** of origin. Then we draw a line parallel to the axis and through P; the distance of the cut point from the y axis to the origin is **y** (Figure II).

Conversely, if we know the coordinates of the point and want to locate it on the plane, we first draw a parallel line for its abscissa and then one for its ordinate towards the axes; These lines intersect at a point that is the one represented by the coordinates P (x, y) (Figure III).