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Comparing Situations by Ratios

Comparing Situations by Ratios
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2020-07-15 18:57
Solid GeometryTransformationGeometric Construction
This example demonstrates comparing different geometric situations through ratios. Core math concepts include ratios, similarity transformations, and geometric constructions. It uses commands like Textfield, Point, Segment, GCD, Sequence in GeoGebra. Suitable for upper elementary or middle school students learning geometric transformations and ratio applications.

GeoGebra Commands & Parameters

  1. Textfield(text4) → InputBox2
  2. Textfield(Q1Jump) → InputBox4
  3. Textfield(text5) → InputBox3
  4. Textfield(Q2Jump) → InputBox5
  5. Point(a) → D
  6. Segment(A, D) → c
  7. Segment(B, C) → d
  8. Text("20%", (scale - 0.25, y(A) + yOffSet)) → text6
  9. Text(8, (scale - 0.12, y(B) + yOffSet)) → text7
  10. GCD(Q1Jump, Q2Jump) → g
  11. Segment(A, I) → i
  12. Segment(B, J) → k
  13. Text(0, (x(A) - 0.12, y(A) - (1.2 * yOffSet))) → text2
  14. Sequence(((e * v), h), v, 0, f) → Q1marks
  15. Sequence(((e * k), 0), k, 0, f) → Q2marks
  16. Sequence(Text[(q * Q1Jump), ((e * q) + topxOffSet, y(B) + yOffSet)], q, 1, f) → TextQ1
  17. Sequence(Text[(p * Q2Jump), ((e * p) + xOffSet, y(A) + yOffSet)], p, 1, f) → TextQ2
  18. Sequence(Text[(q * Q1Jump / 2), ((e / 2 * q) + topxOffSet, y(B) + yOffSet)], q, 1, (f * 2)) → TextQ1split2
  19. Sequence(((e / 2 * l), h), l, 0, (f * 2)) → Q1split2
  20. Sequence(((e / 2 * k), 0), k, 0, (f * 2)) → Q2split2
  21. Sequence(Text[(p * Q2Jump / 2), ((e / 2 * p) + (1.1 * xOffSet), y(A) + yOffSet)], p, 1, (f * 2)) → TextQ2split2
  22. Text(0, (x(B) - 0.12, y(B) + (3.2 * yOffSet))) → text3
  23. Sequence(((e / s * l), h), l, 0, (f * s)) → Q1split
  24. Sequence(((e / s * k), 0), k, 0, (f * s)) → Q2split
  25. Sequence(Text[(q * Q1Jump / s), ((e / s * q) + topxOffSet, y(B) + yOffSet)], q, 1, (f * s)) → TextQ1split
  26. Sequence(Text[(p * Q2Jump / s), ((e / s * p) + xOffSet, y(A) + yOffSet)], p, 1, (f * s)) → TextQ2split

AI Drawing Prompt Reference

Draw a geometric diagram comparing two situations by ratios. Place two starting points on a horizontal baseline, extending two segments to the right to represent initial lengths of two scenarios. Mark each segment with equally spaced tick marks and label them with increasing numbers starting from zero. Above each segment, add text input boxes for two jump amounts. Based on the greatest common divisor of these jumps, subdivide each segment into smaller equal parts and display fractional labels. Below the diagram, annotate percentages like '20%' and '8', and indicate zero positions. The layout should clearly show the division and comparison of ratios.
The prompt above was compiled from the original drawing commands and is for reference only.