Planes In Geometry: The Relationship Between Two Points And A 2-Dimensional Surface

if two points are in a plane

the line containing them is in the plane

If two points are in a plane, then it means that both points lie on the same flat surface or geometric plane. In other words, a plane is a 2-dimensional surface that extends infinitely in all directions. Any two points that are located within this surface are considered to be in the same plane.

For example, if we have points A and B, and they are both located on a piece of paper or whiteboard, then we can consider them to be in the same plane. If we draw a straight line between these two points, it will lie completely within the plane.

It is important to note that there are infinitely many planes that can contain any two points. This is because a plane can be positioned in many different ways, and still pass through both points. Therefore, when discussing the relationship between two points and a plane, it may be necessary to specify which particular plane is being referred to.

Overall, recognizing when two points are in the same plane can be a helpful concept in many areas of mathematics, including geometry and calculus.

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