Collinear points can be joined by the same line.
Point is a notion that can refer to different issues: an orthographic sign, a circle, a place, a topic or a scoring unit are points. Collinear , on the other hand, is used to describe two or more elements that are on the same line .
The notion of collinear points appears in geometry to refer to points that are located on the same line . To understand the concept precisely, then, we must know what a point is in geometry and what a line is.
Analyzing the concept
Both (points and lines), together with the planes , form the set of what is known as fundamental entities of geometry . These are elements that are defined by the bond they establish with similar others.
The point is not a physical element, but rather a figure that lacks surface, volume and length: that is, it has no dimensions, but is used to name a specific position within a space .
The idea of a line or straight line, on the other hand, refers to an infinite succession of points that extends in the same direction and in a single dimension. Straight lines lack a beginning and an end.
The idea of collinear points is used in geometry.
What are collinear points
With all this clear, it is easy to understand what collinear points are. Those points that can be joined by the same line are collinear. In other words: collinear points are those that are joined by a line (the line passes through all of them). That point that is outside the line in question is not collinear with the rest.
Given three points, let's see below how to check if they are collinear through a formula . First of all, it is advisable to graph the points on a plane and define the line segments that can be seen between each pair. Having these values, we can proceed to place two of the points in the distance formula between two points , which is very similar to the one used to calculate the length of the hypotenuse, according to the Pythagorean Theorem: the distance is equal to the square root of the sum of the squares of (x2 – x1) and (y2 – y1) , as shown in the image to the right.
The variables x1 and y1 correspond to the two-dimensional coordinates of the first chosen point, while x2 and y2 are those of the second. To check if we have three collinear points in front of us, we must calculate the distance between each extreme point and the intermediate one, and verify if the sum of both values is equal to the distance between the extreme points.
Although it may seem that using the formula is unnecessary once we make the graph, it is important to note two things: when the values have decimals or when the distance between them is considerable, it is not easy to give a verdict simply by observing them on the plane ; Most experienced people skip this step and use the equation directly, as it saves time and reduces the chances of error.
Applications of the notion
Regarding the applications of this concept, one of the areas closest to the general public that combines the use of mathematics and graphics is the video game industry, and it does so although players do not always notice it. In titles as simple in appearance as target shooting minigames, for example using a slingshot (also known as a slingshot ) as a weapon, the processor needs to constantly calculate the position of various points to, according to code written by the developers , give a response on the screen.
In the case of the slingshot, one of the many techniques to know if the player is aiming correctly can consist of checking if the position of the virtual hand , the midpoint of the fork and the target are collinear.