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H2M 2019 Plane Geometry Question 5

H2M 2019 Plane Geometry Question 5
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2020-06-30 21:39
VectorGeometric Construction
This example demonstrates the application of vectors and linear equations in the 2019 H2M plane geometry question 5. Through constructing vectors, segments, and transformations, it shows how to solve geometric relationships in plane figures. Commands used include Vector, Line, Intersect, Segment, FractionText, and Shear. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Random(1, 2) → c
  2. Random(3, 6) → d
  3. Random(1, 1) → f
  4. Vector(A_1, C_1) → vAC
  5. Vector(B_1, D_1) → vBD
  6. Line(A_1, C_1) → g
  7. Line(B_1, D_1) → h
  8. Intersect(g, h) → X_1
  9. Line(C_1, D_1) → i
  10. Line(O, X_1) → j
  11. Intersect(i, j) → Y_1
  12. Segment(O, X_1) → l
  13. FractionText(Y_1) → textY
  14. Segment(O, Y_1) → k
  15. FractionText(d_1) → textXY
  16. FractionText(X_1) → textX
  17. Shear(B_1, xAxis, 0.5) → B
  18. Shear(C_1, xAxis, 0.5) → C
  19. Shear(D_1, xAxis, 0.5) → D
  20. Shear(A_1, xAxis, 0.5) → A
  21. Shear(X_1, xAxis, 0.5) → X
  22. Shear(Y_1, xAxis, 0.5) → Y
  23. Segment(O, C) → m
  24. Segment(O, Y) → n
  25. Segment(O, D) → p
  26. Segment(C, D) → q
  27. Segment(O, B) → r
  28. Segment(O, A) → s
  29. Segment(B, D) → t
  30. Segment(A, C) → f_1

AI Drawing Prompt Reference

Draw a plane geometry figure with points O, A, B, C, and D, and lines and vectors through these points. First, randomly select points A and C, B and D, then construct vectors vAC and vBD, and lines g and h passing through points A and C, B and D respectively. Find the intersection point X of lines g and h, then construct line i through points C and D, and line j through points O and X, and find their intersection point Y. Next, construct line segments OX and OY, and their fraction texts textXY and textY. Apply shear transformation to points A, B, C, and D to get A', B', C', and D', and construct new line segments AB', AC', BC', CD', AD', and BD'. Finally, construct line segments AB, CD, AD, and BC.
The prompt above was compiled from the original drawing commands and is for reference only.