The extension of a straight line occurs in the same direction.
In the field of geometry , a line is an indefinite and continuous succession of points . The adjective straight , meanwhile, refers to that which has no angles or curves .
A straight line has a single dimension and develops in the same direction . It has an infinite number of points and therefore can extend indefinitely in both directions .
A fundamental entity
Along with the point and the plane , the line is one of the fundamental entities of geometry. This means that it lacks its own definition: it is understood through the description of other elements with similar or similar characteristics.
A straight line is also mentioned as the shortest distance between two points on the same plane. Generally, a straight line is named with a lowercase letter: line a , line b , etc.
The straight line and semi-straight lines
When a straight line is cut, two rays emerge. Each ray is formed by all the points located on one side of the fixed point where the cut occurred (called origin ). In this way, a ray develops indefinitely in a single direction, unlike a straight line.
The two ray lines created by cutting a straight line are classified as opposite . These rays share the origin .
A straight line has no curves.
Confusion of concepts
One of the most common mistakes made by younger students is the assumption that a straight line has a finite length . This is due to several reasons: on the one hand, it is difficult for a child to understand the concept of "infinity", since we do not have any example at hand to observe it, but must accept it in theory; On the other hand, it influences that the graphic representation of this concept does have a beginning and an end.
This leads us to confuse the straight line with the segment and the ray, for example, since all three are represented in similar ways on the school blackboard . Years later, we carry this misunderstanding into our daily lives as adults, unintentionally spreading it into everyday speech. In the field of mathematics , this distortion outside the academic field is very common.
straight line equation
In principle we can study the equation proposed by analytical geometry , the branch of mathematics that focuses on the in-depth study of figures, their areas, distances, volumes, division points and angles of inclination, among other of its many properties. . The equation of the straight line, therefore, is the following: y = mx + b .
The variables x and y are components of a Cartesian plane , a class of orthographic coordinates used to graphically represent certain concepts in mathematics. In this particular case, we must imagine two axes, X and Y , where these variables serve to establish a point.
On the other hand is the m , which is known as the slope of the line , since it affects its inclination with respect to the Cartesian axes. The b , finally, is called the independent term and is the point at which the line crosses the vertical axis.
Use of the notion
In colloquial language , the idea of a straight line is linked to the absence of turns or detours . For example: "The young man entered the room and walked in a straight line to the bar" , "The vehicle headed in a straight line towards the house and ended up hitting the door" .
The usefulness of the concept of a straight line is also something of a mystery, but we can use it for a variety of tasks, ranging from the simple location of various objects in a drawing to the complex process of identifying three-dimensional objects that cannot be seen by the camera. in a video game or a movie.