Coordinate plane: what is it? How to mark points and build figures on the coordinate plane?

Mathematics is a rather complicated science. Studying it, it is necessary not only to solve examples and tasks, but also to work with different figures, and even planes. One of the most used in mathematics is the coordinate system on the plane. Correct work with her children learn 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 the given system is, what actions can be performed with its help, and also learn its main characteristics and features.

Definition of concept

The coordinate plane is the plane on which a certain coordinate system is given. Such a plane is defined by two straight lines intersecting at right angles. At the intersection of these lines is the origin. Each point on the coordinate plane is given by a pair of numbers, which are called coordinates.

In the school course of mathematics, the students have to work closely with the coordinate system - to build figures and points on it, to determine which plane the particular coordinate belongs to, and to determine the coordinates of the point and write down or call them. Therefore, let's talk in more detail about all the features of the coordinates. But first let's talk about the history of creation, and then we'll talk about how to work on the coordinate plane.

Historical reference

The idea of creating a coordinate system was still in the time of Ptolemy. Even then, astronomers and mathematicians were thinking about how to learn to set the position of a point on a plane. Unfortunately, at that time there was still no known coordinate system, and scientists had to use other systems.

Initially, they set the point by specifying latitude and longitude. For a long time this was one of the most widely used methods of mapping a particular information. But in 1637 Rene Descartes created his own coordinate system, later named after the great mathematician "Cartesian".

After the publication of the work "Geometry", Rene Descartes' coordinate system gained recognition in the scientific community.

Already at the end of the XVII century. The notion of "coordinate plane" has become widely used in the world of mathematics. Despite the fact that since the creation of this system several centuries have passed, it is still widely used in mathematics and even in life.

Examples of the coordinate plane

Before talking about the theory, we will give some illustrative examples of the coordinate plane so that you can imagine it yourself. First of all, the coordinate system is used in chess. On the board, each square has its coordinates - one coordinate alphabetic, the second - digital. With its help, you can determine the position of one or another figure on the board.

The second most vivid example is the game "Sea Battle", beloved by many. Remember how, when playing, you call a coordinate, for example, B3, thus indicating exactly where you are aiming. In this case, placing the ships, you specify the points on the coordinate plane.

This coordinate system is widely used not only in mathematics, logic games, but also in military science, astronomy, physics and many other sciences.

Axes of coordinates

As already mentioned, two axes are selected in the coordinate system. Let's talk a little about them, as they are of considerable importance.

The first axis is abscissa - horizontal. It is denoted as ( Ox ). The second axis is the ordinate, which passes vertically through the reference point and is denoted as ( Oy ). These two axes form a coordinate system, dividing the plane into four quarters. The origin is at the intersection of these two axes and takes the value 0 . Only if the plane is formed by two intersecting perpendicular axes having a reference point, this is the coordinate plane.

Also note that each of the axes has its own direction. Usually, when building 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 this concept, like a quarter 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. Thus, in the first quarter the abscissa and ordinate are positive, in the second quarter the abscissa is negative, the ordinate is positive, in the third and abscissa, and the ordinate is negative, in the fourth, abscissa is positive, and the ordinate is negative.

Having remembered these features, you can easily determine to which quarter a particular point belongs. In addition, this information can be useful to you even if you have to do the calculations using the Cartesian system.

Working with the coordinate plane

When we sorted out the concept of the plane and talked about its quarters, you can go to such an issue as working with this system, and also talk about how to put points on it, the coordinates of the figures. On the coordinate plane, this is not so difficult as it might seem at first glance.

First of all, the system itself is built, all important notations are applied to it. Then it's working directly with points or figures. In this case, even when building figures, first the points are drawn on the plane, and then the figures are drawn.

Next, we'll talk in more detail about building a system and directly applying points and shapes.

Rules for constructing a plane

If you decide to start marking figures and points on paper, you will need a coordinate plane. Coordinates of points are applied to it. In order to build a coordinate plane, you only need a ruler and a pen or pencil. First, a horizontal axis of abscissas is drawn, then vertical axis is drawn. It is important to remember that the axes intersect at a right angle.

Next on each axis indicate the direction and sign them using the conventional notation x and y . Also noted is the point of intersection of the axes and is signed with the number 0 .

The next mandatory item is marking. On each of the axes in both directions, unit-segments are marked and signed. This is done so that you can then work with the plane with maximum convenience.

Mark the point

Now let's talk about how to apply the coordinates of points on the coordinate plane. This is the basis that should be known in order to successfully place on the plane various figures, and even to note the equations.

When building points, remember how correctly their coordinates are recorded. So, usually setting the point, two figures are written in brackets. The first digit denotes the coordinate of the point along the abscissa, the second the ordinate.

The point should be constructed this way. First mark the specified point on the Ox axis, then mark the point on the Oy axis. Next, draw imaginary lines from the given notation and find the place of their intersection - this will be the given point.

You will only have to mark it and sign it. As you can see, everything is quite simple and does not require special skills.

We place the figure

Now we turn to the question of how to construct 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 the plane is not so difficult.

First of all you need the coordinates of the points of the figure. It is for them that we will apply to your coordinate system the geometric shapes you have chosen . Consider the application of a rectangle, a triangle, and a circle.

Let's start with a rectangle. Applying it is pretty simple. First, four points are drawn on the plane, denoting the angles of the rectangle. Then all points are connected in series.

The application of a triangle is no different. The only thing - he has three angles, and therefore, on the plane are put three points, denoting its vertices.

Regarding the circle, you should know the coordinates of the two points. The first point is the center of the circle, the second is the point denoting its radius. These two points are placed on the plane. Then compasses are taken, the distance between two points is measured. The point of the compass is placed at the point denoting the center, and a circle is described.

As you can see, there is also nothing difficult here, the main thing is to always have a ruler and compasses at hand.

Now you know how to apply the coordinates of the figures. On the coordinate plane, this is not so difficult as it might seem at first glance.

conclusions

So, we have considered with you one of the most interesting and basic concepts for mathematics, which every schoolboy has to face.

We have found out that the coordinate plane is a plane formed by the intersection of two axes. With its help, you can specify the coordinates of points, apply shapes to it. The plane is divided into quarters, each of which has its own characteristics.

The basic skill that should be worked out when working with the coordinate plane is the ability to correctly apply the given points to it. To do this, you need to know the correct location of the axes, the features of the quarters, and the rules by which the coordinates of the points are specified.

We hope that the information we provided was accessible and understandable, and was also useful for you and helped you to better understand this topic.