# The coordinate axes

Perhaps the best thing to do before explaining the definition and elements present in the coordinate axes is to briefly review some of the concepts that will make it possible to understand this graph, as well as its intention, within its precise context. ## Fundamental definitions

In this sense, it may then be necessary to delimit this revision to two fundamental notions: the first of them, the very concept of Real Numbers, since this will allow us to become aware of the type of element that can be located in the Coordinate Axes. In the second place, it will be convenient to also pay attention to the definition of Numerical line, since the understanding of this graph will make it easier to understand what the coordinate axes consist of. Next, each one of them:

## Real numbers

In this way, we will begin by saying that Mathematics has conceived Real Numbers as those elements that make up the numerical set R, where other numerical sets such as the following are included:

• Natural numbers (N): these numbers constitute the oldest numbers within human civilization. They are used to count the elements of a set, and are composed of all positive integers.
• Integers (Z): in turn, integers constitute the numerical set Z, which in turn includes N, and where positive integers, negative integers and even zero can be counted as elements. In this way, integers will be used to indicate an exact integer quantity, the absence or debt of an integer quantity, or also – through zero- the total absence of quantity.
• Rational numbers: thirdly, within the real numbers there are also rational numbers, which can be expressed either by a fraction (the quotient between two integers) or a decimal number, whose incomplete units are limited or unlimited, but periodic. These numbers are used to account for non-integer quantities.
• The irrational numbers: finally, within the Real Numbers there will be also the irrational Numbers, used to account for non integer or not exact quantities, and whose main characteristic will be to count with incomplete units, conformed by numbers that extend to infinity without there being in them any series of repeated numbers, which in turn means that these numbers cannot be expressed as a fraction.

## Numerical line

For its part, the Numerical Line has been defined as a one-dimensional graph, that is to say that it has only one dimension, and that is composed by a straight line, in which the real Numbers are represented.

In the same way, according to Mathematics, that in this Numerical Line, zero must be placed in the middle, then equidistant points will be placed, that will indicate each one of the integer numbers, both the positive ones, which will be placed to the right; and the negative ones, which will have to be placed to the left. Therefore, the Number Line will be a one-dimensional graph, formed by a graduated line, in which the real numbers (natural, integers, rational and irrational) will be represented graphically.

## The coordinate axes

Once these concepts have been revised, it is perhaps much simpler to approach an explanation of the Coordinate Axes, which are understood by the different mathematical sources as a two-dimensional graph (i.e., representing two dimensions: width and length) made up of two straight perpendicular lines. Its main mission is to serve to locate, according to its specific coordinates, a point or an object in a space of two dimensions, for example a plane or the floor.

## Elements that make up the coordinate axis

According to what the different authors indicate, when enumerating and defining the parts of the Axis of coordinates, it will be necessary to take into account the following three elements:

• Abscissa axis: this is the name of the horizontal line, which will always be represented as the X axis.
• Ordinate axis: on the other hand, this axis will be constituted by the vertical Line, and it will always be represented by the letter Y: the Y axis.
• Origin of coordinates: made up of the point where the two perpendicular lines intersect or cut. It is taken as the reference point, and it is assumed that 0 is located in it, therefore all the points or values located in it are equal to 0. Likewise, Mathematics indicates that these perpendicular straight lines, which correspondingly constitute the axes of the abscissa and the ordinate, must be graduated, constituting then Numeric Rectas that take the Origin of coordinates as the point of origin, from where their positive elements are displayed (located to the right and upwards in the X and Y axes) as well as their negative elements (which will be arranged in the semi-right of the left and downwards).

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