Mathematics - the science is rather complicated.By studying it, we have not only solved examples and problems, but also to work with a variety of figures, and even planes.One of the most commonly used in mathematics is the coordinate system in the plane.Work properly with her children learn more than one year.It is therefore important to know what it is and how to work with it.
Let us see what is the system, what can I do to help her, and know its main characteristics and features.
definition
coordinate plane - is the plane on which a certain system of coordinates.This plane is defined by two straight lines intersecting at right angles.At the point of intersection of these lines is the origin.Each point on the coordinate plane defined by a pair of numbers, called the coordinates.
in school mathematics students have to work quite closely with the coordinate system - to build on it and figures point to determine what belongs to the plane or that coordinate and determine the coordinates of the point, and write or call them.So let's talk more about all the features of the coordinates.But first touch on the history of creation, and then talk about how to work on the coordinate plane.
Background
ideas about creating coordinate systems were still in the time of Ptolemy.Even then, astronomers and mathematicians thought about how to learn to ask the position of points on the plane.Unfortunately, at that time it was not yet known to us the coordinate system, and scientists had to use other systems.
Initially they asked point by specifying latitude and longitude.For a long time it was one of the most used methods of mapping of certain information.But in 1637 Rene Descartes has created its own system of coordinates, called later in honor of the great mathematician "Cartesian".
Following the publication of work "Geometry" Rene Descartes coordinate system gained acceptance in the scientific community.
At the end of the XVII century.the term "coordinate plane" became widely used in the world of mathematics.Despite the fact that since the establishment of this system has been several centuries, it is still widely used in mathematics and even in life.
Examples coordinate plane
Before we talk about the theory, give a few illustrative examples of the coordinate plane, so you can imagine it.The first coordinate system used in chess.On board each square has its own position - one coordinate of the letter, the second - digital.With it you can determine the position of this or that figure on the board.
second most striking example is the much-loved game "Battleship".Remember how, when playing, you name coordinate, for example, B3, thus indicating where exactly are aiming.At the same time, placing ships, you specify the point 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.
Axes
As already mentioned, in the coordinate system secrete two axes.Let's talk a little bit about them, because they are of great importance.
first axis - the abscissa - horizontal.It is referred to as ( Ox ).The second axis - ordinates, which runs vertically through the reference point and is referred to as ( Oy ).These two axes form a coordinate system crashing the plane into four quarters.The origin is at the point of intersection of these two axes, and is set to 0 .Only if the plane is formed by two intersecting perpendicular axes having a point of reference, a coordinate plane.
Also note that each axis has its direction.Typically, the construction of the coordinate system adopted to indicate the direction of the axis of the arrow.Furthermore, the construction of each plane coordinate axes signed.
Quarter
now say a few words about such a concept as a quarter of the coordinate plane.The plane of the two axes is divided into four quarters.Each of them has its own number, and the numbering of the planes being counterclockwise.
Each of the quarters has its own characteristics.Thus, in the first quarter of the abscissa and ordinate is positive in the second quadrant is negative abscissa, ordinate - positive in the third and the abscissa and ordinate of the negative, and the fourth is the abscissa of the positive and negative - ordinate.
remember these features, you can easily determine which quarter is one or another point.In addition, this information may be useful to you and if you have to make calculations using the Cartesian system.
work with the coordinate plane
When we dealt with the concept of the plane and talked about her quarters, you can go to such a problem, how to work with this system, as well as to talk about how to put her point, the coordinates of shapes.On the coordinate plane to make it not so hard as it may seem at first glance.
primarily built the system itself, it bears all the important designation.Then, already is working directly with points or figures.However, even in the construction of figures are put on the plane first point, and then drawn shapes.
Next, we'll talk more about building systems and directly applied to the points and figures.
rules for constructing the plane
If you decide to celebrate on paper figures and terms, you will need to coordinate plane.The coordinates of the points is applied to it.In order to build a coordinate plane, you will need only a ruler and a pen or pencil.First, the horizontal axis is drawn horizontally, then vertically - ordinates.It is important to remember that the axes intersect at right angles.
Next on each axis indicates the direction and sign them by conventional designations x and y .It is also noted the point of intersection of the axes and signed digit 0 .
next must-see destination is the application layout.On each of the axes in both directions marked and signed by the unit-segments.This is done in order to then be able to work with the plane of maximum convenience.
marks the point
Now let's talk about how to apply the coordinates of points on the coordinate plane.This is the basis to be aware of in order to successfully place on the plane of a variety of shapes, and even celebrate the equation.
When constructing points should remember how to record their coordinates.Thus, typically specifying a point in parentheses write two digits.The first digit indicates the coordinate of a point on the x-axis, the second - along the vertical axis.Build
point should be that way.Please note on the axis Ox given point and then mark a point on the axis Oy .Next, draw an imaginary line from the data symbols and find a place of their intersection - this will be a given point.
you just mark it and sign.As you can see, everything is quite simple and does not require special skills.
Place a piece
now turn to this issue, as the construction of the figures on the coordinate plane.In order to build on the coordinate plane any shape, you should know how to place her point.If you know how to do it, then place a figure on the plane is not so difficult.
First of all you need the coordinates of points figure.It is for them we will apply our coordinate system chosen geometric shapes.Consider drawing a rectangle, a triangle and a circle.
Let's start with a rectangle.To put it quite simply.First applied to the four points of the plane, indicating the corners of the rectangle.Then, all points are connected together in series.
Drawing triangle is no different.The only thing - he has three angles, and thus applied to the plane three points, indicating its summit.
Regarding circle here should know the coordinates of two points.The first point - the center of the circle, the second - a point indicating the radius.These two points are plotted on a plane.Then takes a compass, measure the distance between two points.The point of the compass is placed at the point indicating the center and is described by a circle.
As you can see, there is also no big deal, the main thing that has always been at hand ruler and compass.
Now you know how to apply the coordinates of shapes.On the coordinate plane to do it is not so difficult as it might seem at first glance.
Conclusions We have discussed with you one of the most interesting and basic mathematics concepts, faced each student.
We all found that the coordinate plane - is the plane formed by the intersection of two axes.You can use it to set the coordinates of points, to put a figure on it.The plane is divided into quarters, each of which has its own characteristics.
basic skill that should be developed while working with the coordinate plane, - the ability to properly apply it given points.To do this, you should know the correct location of the axes, particularly quarters, as well as the rules by which the coordinates of the points.
We hope that the presentation of the information we had available and understandable, and was useful for you and help to better understand this topic.
