Definition of collinear - What is it, Meaning and Concept

The adjective collinear is used in the field of geometry to qualify the point that is located on the same line as another point .Suppose that, on the line A , it is possible to find the points r , s and t .These three points , therefore, they are collinear: they are on the same line.

To understand precisely what the idea of ​​collinear refers to, we must define terms such as period and straight .The points are geometric figures that, without volume, area, length or dimension, allow to describe a certain position in space, from an already established coordinate system.A straight, on the other hand, is a infinite succession of points that develops in the same direction.

Graphically, a straight is a line that could extend indefinitely both backwards and forwards, always in the same direction.to direction .All the points that are included in that line with collinear lines.If we draw a line B and in it we locate the points k and l , both will be collinear.

On the other hand, if the r point is on the A line and the k point is on the B line , these two points ( r and k ) are not collinear because they both belong to different lines.

It is very important to emphasize that the lines are imaginary and infinite , and in no way are segments that we can draw on a sheet or a wall, but these are part of them, in any case.Therefore, talking about lines and points is not as simple or decisive as talking about objects in the material world, such as being a pencil, which exists and cannot be any other, nor cannot be seen.

However, something shared by a pencil and a straight line is that the name they receive is absolutely arbitrary , both for questions of the language used to name them and for the decision of the speaker at the time to address them: in each language the words used to designate them are different, as well as the phonetic and, why not, the amount of terms needed, but the pencil and a given line remain the same.

In the field of geometry, we can define a two-dimensional plane by means of a formula and then identify one of its infinite lines with the letter R, so as not to miss conventions, but to know if two or more points are collinear, it only matters that they pass the mathematical check, regardless of the name that each one gives to the line or the plane.

When we have only two two-dimensional points and we want to know if they are collinear, we can refer to the equation of the line in question, choose one of its points and check if including it in the formula gives us the rest as a result.For three or more points, we can always group them from a two and calculate their distances, then add the results and compare them with the distance between the furthest ones: if it is the same, then they are all collinear.

segments can also be classified as collinear.Remember that a segment is a portion of a line that develops between two points (called extreme points).When two segments share an extreme point, they are consecutive segments Among them, the collinear segments are those that are located on the same straight line.On the contrary, when the consecutive segments are developed in different lines, we talk about non-collinear segments.

With respect to the operations that we can perform with the collinear segments, if we add two or more consecutive collinear we obtain one that is determined by the uncommon ends of the set.From a geometric point of view, this operation results in a new segment that can be constructed by ordering the originals in a collinear fashion until they find one whose ends are one of each point of the first and the last .