Draw a diagram that contains 5 labeled points, one of which is not coplanar with the other four.

Here is the diagram showing five labeled points. The points \( A \), \( B \), \( C \), and \( D \) are coplanar (lying on the same plane), while point \( E \) is not coplanar with the others, as it is positioned above the plane containing the first four points.

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Here are 8 related questions:
1. What is the definition of coplanar points?
2. How do you determine if a set of points is coplanar?
3. What are some applications of non-coplanar points in geometry?
4. How can vectors be used to prove that points are coplanar?
5. Can more than four points be coplanar in 3D space?
6. What is the significance of the Z-coordinate in determining coplanarity?
7. How would the equation of the plane containing points \( A \), \( B \), \( C \), and \( D \) look?
8. What geometric shapes can be formed by coplanar and non-coplanar points?

**Tip:** When analyzing points in 3D space, checking the determinant of the matrix formed by their position vectors can help determine if they are coplanar.

Learn how to draw a diagram containing five labeled points in 3D space, where one point is non-coplanar with the others. Understand the concept of coplanar points and how to determine coplanarity using vectors and geometric analysis. Suitable for advanced high school students and geometry enthusiasts.

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