coplanar points
points that lie on the same plane
Coplanar points are a set of two or more points that lie on the same plane. In other words, they are points that can be drawn on a flat surface without any of the points overlapping or standing out. A plane can be defined as a flat surface that extends infinitely in all directions.
To determine whether a set of points are coplanar or not, we can use the following steps:
1. Identify the three points in the set that are not collinear, meaning they do not lie on the same line.
2. Draw a plane through these three non-collinear points.
3. Check if the remaining points in the set lie on this plane. If they do, then the points are coplanar.
For example, if we have the set of points A(1,2,3), B(4,5,6), C(7,8,9), and D(10,11,12), we can follow the above steps to determine if they are coplanar or not.
1. We can choose any three non-collinear points, say A, B, and C.
2. Drawing a plane through these three points gives us a flat surface that extends infinitely in all directions.
3. Checking if the remaining point D lies on this plane, we can substitute its coordinates into the equation of the plane to see if it satisfies the equation. If it does, then it lies on the plane and the points are coplanar.
Overall, coplanar points are a fundamental concept in geometry and are useful in many different areas of mathematics and science.
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