In the image, you're asked to determine which set of points are coplanar from a 3D cube.

Coplanar points are points that lie on the same geometric plane. Let's analyze each option:

1. AHBC: Points A, H, B, and C do not lie on the same face of the cube. Hence, they are not coplanar.

2. DCBE: Points D, C, B, and E all lie on the top face of the cube. These points are coplanar.

3. AHCD: Points A, H, C, and D are not on the same face, so they are not coplanar.

4. EDCA: Points E, D, C, and A form a diagonal plane that cuts through the cube, but they are not coplanar on any cube face.

The correct answer is DCBE.

Would you like further details on the concept of coplanarity? Here are some related questions:

1. How do you define a geometric plane in 3D space?
2. Can three points in space ever be non-coplanar?
3. How can you determine if four points in space are coplanar mathematically?
4. What is the difference between collinear and coplanar points?
5. How does the shape of a cube help in visualizing planes?

Tip: In a cube, each face represents a plane, and any four points on a face will always be coplanar.