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Cartesian plane

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In the area of ​​mathematics, the Cartesian coordinate system or rectangular coordinate system as it is also known, is used to determine each point in a unique way within a plane by means of two numbers , which are generally called the x coordinate and the y coordinate of the point. To define this type of coordinates, two perpendicular directed lines are specified , the x-axis or the abscissa and the y-axis the ordinate , as well as the lengthof the unit, which is marked on both axes. Cartesian coordinate systems can also be used in space where three coordinates are used and in higher dimensions.

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What is the Cartesian plane?

The Cartesian plane are two number lines in perpendicular position , one of them horizontal and the other vertical , which intersect at a point known as the origin or zero of the system.

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  • Characteristics of the Cartesian plane
  • What is it for
  • Source
  • History
  • Parts of the Cartesian plane
  • Quadrants
  • How to make a Cartesian plane
  • Location of points on the Cartesian plane
  • Importance
  • Example

Characteristics of the Cartesian plane

The main characteristics that we can observe in a Cartesian plane are the following:

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  • The Cartesian plane is formed by four different quadrants or areas that are the product of the union between two perpendicular lines or orthogonal coordinates.
  • It has two axes that are also known as the abscissa axis .
  • One of its axes is located horizontally and is identified by the letter X.
  • The ordinate axis is located vertically and is represented by the letter Y.
  • It is characterized by the union of two perpendicular lines that divide a plane into four different quadrants.
  • Its purpose is to be able to describe the position of two points represented by the coordinates or ordered pairs .

What is it for

The Cartesian plane helps us to locate pairs of points that are known by the name of coordinates which are formed with an X value and a Y value.   It also serves to be able to make an analysis of some of the geometric figures such as the parabola, hyperbole , line, circumference, and the eclipse, which are all part of analytic geometry .  It also works as a reference in any plane that exists.

Source

The origin of the Cartesian plane was born with René Descartes, who in turn was the creator of analytical geometry.

History

The history of the Cartesian plane originated when Descartes took a starting point in the Cartesian reference system in order to represent the plane geometry that existed between two perpendicular lines , which intersected at a certain point that he called coordinates .

Parts of the Cartesian plane

The parts that the Cartesian plane has are the following:

  • The horizontal line : the term refers to the abscissa or axis and is represented by the letter X.  The points that are located on the abscissa axis have their ordinate that is equal to 0 while the points that They are located on the ordinate axis and have their abscissa equal to the value 0. The points found on the same vertical line , which is parallel to the ordinate axis, have the same abscissa .
  • The vertical line: it   is also known as the ordinate or yes , it is represented by the letter y. The points that are located on the ordinate axis have their abscissa equal to the value 0.
  • The point of intersection : this point is responsible for dividing or cutting the two vertical and horizontal lines, it is also known by the name of origin .

Quadrants

The Cartesian plane is generally divided into four parts that are known as quadrants . These quadrants are organized in an anti-clockwise direction, that is, they go counterclockwise. They are called the first, second, third and fourth quadrants respectively.

  • The first quadrant is the one that is located in the upper right part and that includes only positive numbers on the ordinate axis.
  • The second quadrant is located in the upper left part and includes only the positive numbers of the Y ordinate axis.
  • The third quadrant is that it is located in the lower left part and in this place only the negative numbers of the two axes are taken into account .
  • The last quadrant is at the bottom of the Cartesian plane and encompasses negative numbers .

How to make a Cartesian plane

The steps to be able to make a Cartesian plane are the following:

  • Remember that the X axis goes to the left and right, and the second coordinate is on the Y axis. Also, positive numbers go to the right and negative numbers go to the left.
  • Locate the quadrants of the Cartesian plane.
  • Begin to graph a point at zero that is the intersection between the X axis and the Y axis.
  • If the coordinates are positive it should be moved to the right , if they are negative to the left .
  • Then the point is marked .

Location of points on the Cartesian plane

In order to locate or locate the points in a Cartesian plane we must follow the following procedure:

  • First, to be able to locate the abscissa or the value of x , the units that correspond to the right if they are positive or to the left in case they are negative must be counted , this from the point of origin, in this case the number zero.
  • From the point where the value of X was located, the corresponding units must be counted up if they are positive or down if they are negative so that any point can be located depending on its coordinates .

In order to determine the coordinates of a given point in the Cartesian plane, the units that correspond on the x- axis to the right or to the left must be found depending on whether they are negative or positive .

Importance

The importance of the Cartesian plane lies in the fact that it can represent points or figures in different coordinates . In the area of physics it is very important because it is the means by which it is known how forces can affect a point, how electromagnetism affects the charges that a particle has.

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