Understanding Coplanar Points: Definition, Examples, and Importance in Geometry and Coordinate Geometry

Coplanar points

Coplanar points refer to a set of points that all lie in the same plane

Coplanar points refer to a set of points that all lie in the same plane. In geometry, a plane is a flat, two-dimensional surface that extends infinitely in all directions. So, if you have a group of points that all lie in the same plane, they are considered coplanar.

To understand this concept better, let’s consider an example. Imagine you have three points: A, B, and C. If you can draw a flat surface or a plane that contains all three points, then A, B, and C are coplanar. In other words, you can place a sheet of paper on the points A, B, and C in such a way that the paper would cover all the points without crossing through them.

It is also important to note that any two points are always coplanar since any two points can be connected by a line segment, and a line segment lies in a plane. However, when dealing with more than two points, you need to consider if a single plane can contain all the points.

On the contrary, if you have a group of points that do not lie in the same plane, they are called non-coplanar points. In such cases, you cannot draw a flat surface or plane that contains all the points without some points being outside the plane.

To summarize, coplanar points are points that lie in the same plane, whereas non-coplanar points are points that do not lie in the same plane. Understanding and identifying coplanar points is important in various areas of math, such as geometry and coordinate geometry.

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