Prior to advancing in an explanation about the Coordinates of a point, it may be convenient to make a brief revision about the definition given by Mathematics about the Axes of coordinates, because this may help to understand what the coordinates of a point are, and how they should be represented.
In this way, we will begin by saying that the coordinate axes can be understood as a two-dimensional graph (that is, that it has two dimensions: for example, width and length) made up of two straight perpendicular lines. According to what the mathematical discipline indicates, the main objective of this graph is to help represent, in a plane, the exact location of a point in space.
With respect to the elements that make up the Coordinate Axes, the different authors have also pointed out that these can be considered three, each of which will receive the following denomination, and will be located in the places indicated below:
Abscissa axes: this axis will be constituted by the horizontal straight line. It is represented by the letter Y.
Ordinate axes: on the other hand, the axis of the ordinate will form the vertical line. It will be represented by the letter Y.
Origin of coordinates: finally, the point where these two lines intersect will be known as the Origin of coordinates. According to what Mathematics points out, every point located in the Origin of coordinates will be taken as zero.
Also, the diverse authors have indicated that these equidistant straight lines will be graduated, constituting in itself two numerical Rectas: one horizontal, and another vertical. These lines will take the origin of coordinates as the zero, extending to the right and upwards the positive numbers, while the negative ones will be located towards the semi-right of the left and the one located downwards).
Coordinates of a point
Once the concept of coordinate axes has been revised, it is perhaps much easier to explain the coordinates of a point, which must be understood as the exact data that allow an object or point to be located within a plane of coordinates or an axis of coordinates. That is, it is the direction of location of a point on a two-dimensional plane.
When located in a two-dimensional plane, then the coordinates of the point to be located will always be constituted by a pair of numbers or data, which will be expressed in the form (a,b). In this sense, Mathematics has expressed that the data a will always be equivalent to the number corresponding to the abscissa axis, that is to say the horizontal axis X, while the data b, will correspond without variation to the number that must be located in the vertical axis Y. The number a will always be equivalent to the number corresponding to the abscissa axis, that is to say the horizontal axis X, while the data b, will correspond without variation to the number that must be located in the vertical axis Y. The union of these two data in the plane of coordinates will represent the exact location of a point or an object in this two-dimensional plane.
Example of the coordinates of a point
However, it may be best to explain exactly how the coordinates of a point are located on an axis of coordinates through a precise example,which allows us to see in a practical way how this exercise should be performed, as seen below:
Given the coordinates (4,6), place the corresponding point on the Coordinate axis:
In this order of ideas, the first thing that should be done is to draw an Axis of coordinates, in which it is possible to express its horizontal axis (x) and the vertical axis (Y), as well as the values that go from 0 to 6, so that both points have representation in the two axes:
Phoneia.com (October 31, 2019). Coordinates of a point. Recovered from https://phoneia.com/en/education/coordinates-of-a-point/