https://file.aiquickdraw.com/mathbot/file/1729823577768nut65615.jpg

The image shows a 3D coordinate system with the X, Y, and Z axes labeled. The points to be marked are given in the problem as follows:

- P (0,0,2)
- Q (0,2,2)
- R (2,1,2)
- S (-2,-1,2)

Let's break down where each point would be located on the 3D graph:

1. **Point P (0,0,2)**: This point is directly on the Z-axis, 2 units above the origin (0,0,0).
2. **Point Q (0,2,2)**: This point has no X-component, is 2 units along the Y-axis, and 2 units up along the Z-axis.
3. **Point R (2,1,2)**: This point is 2 units along the X-axis, 1 unit along the Y-axis, and 2 units up along the Z-axis.
4. **Point S (-2,-1,2)**: This point is -2 units along the X-axis, -1 unit along the Y-axis, and 2 units up along the Z-axis.

You can now mark these points on the graph by projecting each coordinate to its corresponding axis and point.

Would you like to see an image of how these points look marked on this 3D graph?

Here are 5 follow-up questions:
1. How do we calculate the distance between two points in a 3D coordinate system?
2. What is the difference between plotting points in 2D versus 3D?
3. How can you determine if a point lies on a particular plane?
4. What is the equation of a plane in 3D that contains three specific points?
5. How can you find the centroid of a group of points in 3D space?

**Tip**: To visualize points in 3D, always start by focusing on one axis at a time (X, Y, or Z) and track how far each point is from the origin along each axis.

Marque sobre la figura los siguientes puntos: P(0,0,2), Q(0,2,2), R(2,1,2), S(-2,-1,2)

Learn how to plot points on a 3D coordinate system with this example. The points P(0,0,2), Q(0,2,2), R(2,1,2), and S(-2,-1,2) are marked step by step. Suitable for students in Grades 9-12.

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