Mathematics is a rather complicated science. Studying it, one has not only to solve examples and problems, but also to work with various figures, and even planes. One of the most used in mathematics is the coordinate system on the plane. Children have been taught how to work with it correctly for more than one year. Therefore, it is important to know what it is and how to work with it correctly.
Let's figure out what this system is, what actions you can perform with it, and also find out its main characteristics and features.
Definition of concept
Coordinate plane is a plane on which a certain coordinate system is set. Such a plane is defined by two straight lines intersecting at a right angle. The point of intersection of these lines is the origin of coordinates. Each point on the coordinate plane is given by a pair of numbers, which are called coordinates.
In the school course of mathematics, schoolchildren have to work quite closely with the coordinate system - to build figures and points on it, to determine whichone or another coordinate belongs to the plane, as well as to determine the coordinates of a point and write or name them. Therefore, let's talk in more detail about all the features of the coordinates. But first, let's touch on the history of creation, and then we'll talk about how to work on the coordinate plane.
Historical background
Ideas about creating a coordinate system were in the days of Ptolemy. Even then, astronomers and mathematicians were thinking about how to learn how to set the position of a point on a plane. Unfortunately, at that time there was no coordinate system known to us, and scientists had to use other systems.
Initially they set points using latitude and longitude. For a long time it was one of the most used ways of mapping this or that information. But in 1637, Rene Descartes created his own coordinate system, later named "Cartesian" in honor of the great mathematician.
After the publication of the work "Geometry", the coordinate system of Rene Descartes won recognition in scientific circles.
Already at the end of the 17th century. the concept of "coordinate plane" has become widely used in the world of mathematics. Despite the fact that several centuries have passed since the creation of this system, it is still widely used in mathematics and even in life.
Coordinate plane examples
Before we talk about the theory, let's give some illustrative examples of the coordinate plane so that you can imagine it. The coordinate system is primarily used in chess. On the board, each square has its own coordinates - one letter coordinate, the second - digital. With its help, you can determine the position of a particular piece on the board.
The second most striking example is the beloved game "Battleship". Remember how, when playing, you name a coordinate, for example, B3, thus indicating exactly where you are aiming. At the same time, when placing ships, you set points on the coordinate plane.
This coordinate system is widely used not only in mathematics, logic games, but also in military affairs, astronomy, physics and many other sciences.
Coordinate axes
As already mentioned, there are two axes in the coordinate system. Let's talk a little about them, as they are of considerable importance.
The first axis - abscissa - is horizontal. It is denoted as (Ox). The second axis is the y-axis, which passes vertically through the reference point and is denoted as (Oy). It is these two axes that form the coordinate system, dividing the plane into four quarters. The origin is located at the point of intersection of these two axes and takes the value 0. Only if the plane is formed by two perpendicularly intersecting axes that have a reference point, is it a coordinate plane.
Also note that each of the axes has its own direction. Usually, when constructing a coordinate system, it is customary to indicate the direction of the axis in the form of an arrow. In addition, when constructing the coordinate plane, each of the axes is signed.
Quarters
Now let's say a few words about such a concept as quarters of the coordinate plane. The plane is divided by two axes into four quarters. Each of them has its own number, while the numbering of the planes is counterclockwise.
Each of the quarters has its own characteristics. So, in the first quarter, the abscissa and the ordinate are positive, in the second quarter, the abscissa is negative, the ordinate is positive, in the third, both the abscissa and the ordinate are negative, in the fourth, the abscissa is positive, and the ordinate is negative.
By remembering these features, you can easily determine which quarter this or that point belongs to. In addition, this information may be useful to you if you have to do calculations using the Cartesian system.
Working with the coordinate plane
When we figured out the concept of a plane and talked about its quarters, we can move on to such a problem as working with this system, and also talk about how to put points, coordinates of figures on it. On the coordinate plane, this is not as difficult as it might seem at first glance.
First of all, the system itself is built, all important designations are applied to it. Then there is work directly with points or figures. In this case, even when constructing figures, points are first applied to the plane, and then the figures are already drawn.
Next, we'll talk more about building a system and directly applying points and shapes.
Rulesplane construction
If you decide to start marking shapes and points on paper, you will need a coordinate plane. The coordinates of the points are plotted on it. In order to build a coordinate plane, you only need a ruler and a pen or pencil. First, the horizontal abscissa is drawn, then the vertical - ordinate. It is important to remember that the axes intersect at right angles.
Further, on each axis indicate the direction and sign them using the generally accepted notation x and y. The point of intersection of the axes is also marked and signed with the number 0.
The next obligatory item is marking. Units-segments are marked and signed on each of the axes in both directions. This is done so that you can then work with the plane with maximum convenience.
Marking a point
Now let's talk about how to plot the coordinates of points on the coordinate plane. This is the basics you need to know to successfully place a variety of shapes on the plane, and even mark equations.
When plotting points, remember how their coordinates are written correctly. So, usually setting a point, two numbers are written in brackets. The first digit indicates the coordinate of the point along the abscissa axis, the second - along the ordinate axis.
Build a point in this way. First, mark a given point on the Ox axis, then mark a point on the Oy axis. Next, draw imaginary lines from these designations and find the place of their intersection - this will be the given point.
You just have to mark it and sign it. As you can see, everything is quite simple and does not require special skills.
Place the shape
Now let's move on to such a question as the construction of figures on the coordinate plane. In order to build any figure on the coordinate plane, you should know how to place points on it. If you know how to do this, then placing a figure on a plane is not so difficult.
First of all, you will need the coordinates of the points of the shape. It is on them that we will apply the geometric shapes you have chosen to our coordinate system. Consider drawing a rectangle, triangle and circle.
Let's start with a rectangle. Applying it is pretty easy. First, four points are applied to the plane, indicating the corners of the rectangle. Then all points are sequentially connected to each other.
Drawing a triangle is no different. The only thing is that it has three corners, which means that three points are applied to the plane, denoting its vertices.
Regarding the circle, here you should know the coordinates of two points. The first point is the center of the circle, the second is the point denoting its radius. These two points are plotted on a plane. Then a compass is taken, the distance between two points is measured. The point of the compass is placed at a point indicating the center, and a circle is described.
As you can see, there is nothing complicated here either, the main thing is to always have a ruler and a compass at hand.
Now you know how to plot shape coordinates. On the coordinate plane, this is not so difficult to do as it might seem at first glance.
Conclusions
So, we have considered with you one of the most interesting and basic concepts for mathematics that every student has to deal with.
We have found out that the coordinate plane is the plane formed by the intersection of two axes. With its help, you can set the coordinates of points, put shapes on it. The plane is divided into quarters, each of which has its own characteristics.
The main skill that should be developed when working with the coordinate plane is the ability to correctly plot given points on it. To do this, you should know the correct location of the axes, the features of the quarters, as well as the rules by which the coordinates of the points are set.
We hope that the information presented by us was accessible and understandable, and was also useful for you and helped you better understand this topic.
