Points D, E, And F Are Not In A Line: Understanding Non-Collinear Points


Geometry is one of the oldest branches of mathematics, and it deals with the study of shapes, sizes, positions, and dimensions of objects in space. One of the fundamental concepts in geometry is the notion of collinearity, which refers to the property of points lying on a single line. In this article, we will explore the concept of non-collinearity and its implications for geometry.

What Are Non-Collinear Points?

Non-collinear points are points that do not lie on a single line. In other words, there is no straight line that passes through all of them. Points D, E, and F are an example of non-collinear points, as shown in the diagram below.

Non-Collinear Points

Properties of Non-Collinear Points

Non-collinear points have several properties that distinguish them from collinear points. One of the most important properties is that they determine a plane. In other words, any three non-collinear points uniquely define a plane in three-dimensional space. Another property of non-collinear points is that they cannot be connected by a line segment. Instead, we need to use multiple line segments or curves to connect them. This is because a line segment is defined as the shortest path between two points, and there is no shortest path between non-collinear points.

Applications of Non-Collinear Points

Non-collinear points have many applications in geometry and other fields. For example, they are used in computer graphics to create three-dimensional models of objects. Non-collinear points are also used in surveying and mapping to determine the position of objects relative to each other. In addition, non-collinear points are used in cryptography to generate random numbers and to create secure communication channels. The randomness of non-collinear points makes them ideal for encryption and decryption algorithms.

Examples of Non-Collinear Points

Non-collinear points can be found in many shapes and structures. For example, the vertices of a triangle are always non-collinear, as shown in the diagram below.

Non-Collinear Points in a Triangle

Other examples of non-collinear points include the corners of a cube, the vertices of a tetrahedron, and the points on a circle that do not lie on its diameter.


In conclusion, non-collinear points are an important concept in geometry that has many applications in various fields. Understanding the properties and applications of non-collinear points can help us better understand the world around us and solve complex problems. Points D, E, and F are just one example of non-collinear points, and there are many more to discover and explore.