Euler's Eyes
2022-09-13
Cartesian Plane
Coordinates you can test
Choose an entire entry. The horizontal position is x; the vertical is f(x). Find the point (−2, −5) using a = 2 and b = −1.
Em telas pequenas, deslize o gráfico na horizontal para ler os detalhes.
The Cartesian plane was successfully proposed by René Descartes, in which it is composed of two perpendicular lines. Here, we are going to talk about these two number lines, which in this context, are whole numbers. In later posts, we will talk about other numerical sets.
Preliminary definitions
The two lines that make up the Cartesian plane are numerical lines that we define below:
Definition: Abscissa is the horizontal number line, which we call the coordinate of the $x$ axis.
Definition: Ordinate is the vertical number line, which we call the axis coordinate $y$.
Ordered pair
Definition: Ordered pair is two numbers formed by the pair $(x,y)$ with coordinates $x$ and $y$ respectively.
Quadrants
After defining ordered pairs, the next step is to classify these pairs. In a counterclockwise direction we can classify these pairs that we call quadrants. In this way, we have the quadrants:
- First quadrant: ordered pairs $(x,y)$ both positive
- Second quadrant: ordered pairs $(-x,y)$ negative abscissa > and positive ordinate
- Third quadrant: ordered pairs $(-x,-y)$ both negative
- Fourth quadrant: ordered pairs $(x,-y)$ positive abscissa and negative ordinate
First Quadrant Example
The ordered pair $(x,y) = (3,1)$ is represented as follows in the Cartesian plane:
Second Quadrant Example
The ordered pair $(x,y) = (-2,1)$ is represented as follows in the Cartesian plane:
Third Quadrant Example
The ordered pair $(x,y) = (-1,-1)$ is represented as follows in the Cartesian plane:
Fourth Quadrant Example
The ordered pair $(x,y) = (4,-1)$ is represented as follows in the Cartesian plane:
Applications of the Cartesian Plane
In many applications the Cartesian plane is very useful, as it serves as a reference system for locating points on the plane.
In major professions such as statistics, chemical engineering, medicine, the Cartesian plane is used through graphics using functions.
The functions, as said in the previous post, the act of listening and speaking represent what we call function today. In this way, René Discards used an ear as a symbol.
- Say what you hear twice;
- We can observe that the symbology (semiotically active language of an ear).
In architecture and civil construction, the Cartesian plan is used as a basis for drawing up plans for houses and buildings.
The GPS (global positioning system) global positioning system is widely used today. Previously used in navigation, aviation. Today, any car user cannot live without GPS. This important system is based on the Cartesian coordinate system.
The positions of this system are determined through its geographic coordinates (latitude, longitude and altitude).
In this case, it is a more complex system than the one presented in this post, as it is a three-dimensional Cartesian system (x,y,z). These systems use satellites to determine these coordinates in the Cartesian plane.
Here we talk all about the Cartesian plane. Wait for the next posts.