Cartesian Plane (Meaning and Explanation)

We explain what the Cartesian plane is, how it was created, its quadrants and elements. Also, how functions are represented.

What is the Cartesian plane?

The Cartesian plane or Cartesian system is called a diagram of orthogonal coordinates used for geometric operations in Euclidean space (that is, the geometric space that meets the requirements formulated in ancient times by Euclid).

It is used for graphing mathematical functions and analytic geometry equations. It also allows us to represent relationships of movement and physical position.

It is a two-dimensional system, consisting of two axes that extend from an origin to infinity (forming a cross). These axes intersect at a single point (denoting the coordinate origin point or point 0,0).

A set of longitude marks are drawn on each axis, which serve as a reference to locate points, draw figures or represent mathematical operations. In other words, it is a geometric tool to put the latter in relation graphically.

The Cartesian plane owes its name to the French philosopher René Descartes (1596-1650), creator of the field of analytical geometry.

History of the Cartesian plane

rene descartes cartesian plane — René Descartes created the Cartesian plane in the 17th century.

The Cartesian plane It was an invention of René Descartes as we have said, central philosopher in the Western tradition. His philosophical perspective was always based on the search for the point of origin of knowledge.

What is the Cartesian plane used for?

cartesian plane characteristics — Coordinates allow you to locate points on the Cartesian plane.

The Cartesian plane is a diagram in which we can locate points, based on their respective coordinates on each axis, just as a GPS does on the globe. From there, too movement can be represented graphically (the displacement from one point to another in the coordinate system).

Besides, allows you to draw two-dimensional geometric figures from straight lines and curves. These figures correspond to certain arithmetic operations such as equations, simple operations, etc.

There are two ways to resolve these operations: mathematically and then graphing it, or we can find a solution graphically, since there is a clear correspondence between what is illustrated on the Cartesian plane, and what is expressed in mathematical symbols.

In the coordinate system, to locate the points we need two values: the first corresponding to the horizontal X axis and the second to the vertical Y axis which are denoted in parentheses and separated by a comma: (0,0) for example, is the point where both lines intersect.

These values can be positive or negative, depending on their location with respect to the lines that make up the plane.

Quadrants of the Cartesian plane

quadrant cartesian plane — The X and Y axes divide the Cartesian plane into four quadrants.

As we have seen, the Cartesian plane is constituted by the intersection of two coordinate axes, that is, two infinite straight lines, identified with the letters x (horizontal) and on the other hand and (vertical). If we look at them, we will see that they form a kind of cross, thus dividing the plane into four quadrants, which are:

Quadrant I. In the upper right region, where positive values can be represented on each coordinate axis. For example: (1,1).
Quadrant II. In the upper left region, where positive values can be represented on the axis and but negative in the x. For example: (-1, 1).
Quadrant III. In the lower left region, where negative values can be represented on both axes. For example: (-1,-1).
Quadrant IV. In the lower right region, where negative values can be represented on the axis and but positive in the x. For example: (1, -1).

Elements of the Cartesian plane

The Cartesian plane is made up of two perpendicular axes, as we already know: the ordinates (axis and) and the abscissa (axis x). Both lines extend to infinity, both in their positive and negative values. The only one Crossing point between both is called origin (coordinates 0.0).

Starting from the origin, each axis is marked with values expressed in whole numbers. The point of intersection of any two points is called a point. Each point is expressed in its respective coordinates always saying the abscissa first and then the ordinate. By joining two points you can build a line, and with several lines you can build a figure.

Functions in a Cartesian plane

cartesian plane function — Functions can be expressed graphically in the Cartesian plane.

Mathematical functions can be expressed graphically in a Cartesian plane as long as we express the relationship between a variable x and a variable and so that it can be resolved.

For example, if we have a function that states that the value of and will be 4 when the of x be 2, we can say that we have a function expressible like this: y = 2x. The function indicates the relationship between both axes, and allows giving value to one variable knowing the value of the other.

For example if x = 1, then y = 2. On the other hand, if x = 2, then y = 4, if x = 3, then y = 6, etc. By finding all those points in the coordinate system, we will have a straight line, given that the relationship between both axes is continuous and stable, predictable. If we continue the straight line towards infinity, we will then know what the value of x in any case of and.

The same logic will apply to other types of functions, more complex, which will yield curved lines, parabolas, geometric figures or discontinuous lines, depending on the mathematical relationship expressed in the function. However, the logic will remain the same: express the function graphically based on assigning values to the variables and solving the equation.