3D Coordinate System: Point and Prism Construction

3D Coordinate System: Point and Prism Construction
Loading the math board and drawing, please wait…
2021-08-11 13:27
This example demonstrates how to plot points in a 3D coordinate system and construct prism solid models. Core mathematical concepts include spatial coordinate systems, three-dimensional vectors, prism properties in solid geometry, and relationships between polygons and spatial planes. Construction highlights: Based on the construction summary, this example uses Point command to define points in 3D space, Plane command to create coordinate planes, Polygon command to draw base polygons, Prism command to generate prisms, Midpoint command to mark midpoints of edges, Segment command to draw line segments, OrthogonalLine command to construct perpendicular lines, and Intersect command to find intersections, ultimately building a complete 3D geometric figure with multiple faces (faceANMO, faceIMOP, etc.) and edges (edgeAN, edgeMO). Suitable for high school and college students learning spatial analytic geometry, understanding 3D coordinate systems, and developing spatial visualization skills.

GeoGebra Commands & Parameters

  1. Intersect(yAxis, zAxis) → D
  2. Point(xAxis) → E
  3. Point(yAxis) → F
  4. Point(zAxis) → B
  5. Plane(D, F, B) → p
  6. Plane(D, E, B) → r
  7. OrthogonalLine(A, r) → f
  8. OrthogonalLine(A, p) → g
  9. Intersect(f, r) → C
  10. Intersect(g, p) → G
  11. OrthogonalLine(C, p) → h
  12. OrthogonalLine(G, r) → i
  13. Intersect(h, i) → H
  14. Intersect(yAxis, xAxis) → I
  15. Point(yAxis) → J
  16. Point(xAxis) → K
  17. Plane(I, J, K) → q
  18. OrthogonalLine(C, q) → j
  19. OrthogonalLine(G, q) → k
  20. OrthogonalLine(A, q) → l
  21. Intersect(j, xAxis) → L
  22. Intersect(k, yAxis) → M
  23. Intersect(l, q) → N
  24. Polygon(N, M, I, L) → q1, n, m, i_1, l_1
  25. Prism(q1, A) → a, O, edgeMO, edgeIP, edgeLQ, edgeAO, edgeOP, edgePQ, edgeAQ, P, Q, faceANMO, faceIMOP, faceILQP, faceANLQ, faceAOPQ, edgeAN
  26. Midpoint(edgeAQ) → R
  27. Midpoint(edgeAO) → S
  28. Midpoint(edgeAN) → T
  29. Segment(L, N) → s
  30. Segment(N, M) → t

AI Drawing Prompt Reference

Draw a 3D coordinate system with key points located on the coordinate axes, then define two planes using three points each and use perpendicular constructions to find additional intersection points on/among these planes. Using the appropriate four intersection points on one plane, construct a quadrilateral as the base. From this base and a reference point associated with the axis-origin direction, build a prism solid. Finally, mark midpoints on selected prism edges and draw a couple of segments between base intersection points to emphasize how the base edges relate to the 3D prism structure.
The prompt above was compiled from the original drawing commands and is for reference only.