O Cartesian plane is a flat mathematical object composed of two number linesperpendicular, that is, straight lines that have only one point in common, forming a angle 90°. This common point is known as the origin and it is there that the number zero of both lines is marked. The Cartesian plan received this name because it was conceived by Rene Descartes and it is used fundamentally to systematize location techniques in the plane.
Numerical lines: abscissa and ordinate
The two lines that give rise to the Cartesian plane must be number lines, as this is the condition that will make it possible to find locations of any points on the plane. This location is the fundamental basis of much common knowledge in everyday life, such as distance between points.
A number line is an ordinary line in which a correspondence has been established with the real numbers. In this way, each point on the line is linked to a single real number and it is this fact that allows any location. Any real number will have only one location along the entire infinite length of the line.
The Cartesian plane is formed by two of these lines: One responsible for the horizontal coordinate and the other responsible for the vertical coordinate. It is common to use the letters x for the first and y for the second and the terms “x coordinate” and “y coordinate”.
In the Cartesian plane, the vertical line responsible for the y coordinates is called ordered, and the horizontal line, responsible for the x coordinates, is called abscissa.
Cartesian plane with emphasis on the abscissa and the ordinate
Ordered pairs and locations in the plane
An ordered pair is made up of two real numbers that represent a coordinate. The order chosen is as follows: First come the x coordinates and then the y coordinates, which are enclosed in parentheses to represent any location. For example, look at the following image:
Note that point A has coordinates x = 2 and y = 3. If a point is given so that its location is marked on the plane, such as point B = (3, -3), we must first draw a vertical line over the number 3 on the abscissa axis (x coordinates). This is because the first coordinate is always the x coordinate. Afterwards, we draw a horizontal line over the number – 3 on the ordinate axis (y coordinates):
Point B is the meeting between the drawn horizontal lines, as illustrated in the image above.
quadrants
As it is formed by two numerical lines, there are some peculiarities of the Cartesian plane. Rightmost points have x-coordinate greater than leftmost points. Upward points have a y-coordinate greater than downside numbers.
Also, the region where x and y are positive simultaneously is called the first quadrant. The region where y is positive and x is negative is known as second quadrant. The region where x and y are negative simultaneously is called the third quadrant. Finally, when x is positive and y is negative, the points are located on the fourth quadrant.
These quadrants are numbered counterclockwise, starting from the first quadrant, which is to the right of the y axis and above the x axis, as shown in the following figure:
By Luiz Paulo Moreira
Graduated in Mathematics
Source: Brazil School - https://brasilescola.uol.com.br/o-que-e/matematica/o-que-e-plano-cartesiano.htm
