Definition of Collinear Points
Collinear points are a set of two or more points that lie on the same single straight line. The term 'collinear' literally means 'together on a line.' In two-dimensional or three-dimensional space, if points can be connected by one continuous straight line, they are considered collinear.
Key Principles of Collinearity
The fundamental principle is that a unique straight line can always be drawn through any two distinct points. If a third point also lies on this *same* line, then all three points are collinear. If the third point does not lie on that line, then the three points are non-collinear, defining a plane (in 3D) or forming a triangle (in 2D).
Practical Example of Collinear Points
Imagine a ruler placed on a piece of paper. If you mark three dots (A, B, and C) exactly along the edge of the ruler, those three dots are collinear. If you move dot C slightly off the ruler's edge, then points A, B, and C are no longer collinear, as a single straight line cannot pass through all three.
Importance and Applications
Understanding collinearity is fundamental in geometry and various STEM fields. It's crucial for defining lines, segments, and rays, and for proving geometric theorems. In physics, if forces are collinear, they act along the same line, simplifying vector addition. In computer graphics, collinearity is used in algorithms for line detection and object alignment.