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Quiz on Proportional Relationships: Visualizing Linear Scaling with Geometry

Quiz on Proportional Relationships: Visualizing Linear Scaling with Geometry
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2021-04-08 22:31
VectorFunctionTransformationGeometric ConstructionSlider Animation
In collections Proportional Relationships
This GeoGebra example presents an interactive quiz that demonstrates how proportional relationships remain consistent across both geometric configurations and numerical correspondences. It focuses on key ideas such as linear proportionality, vector-based reasoning, and geometric dilation (scaling) to generate corresponding points and segments. The construction is driven by randomized parameters (Random) to create multiple cases, then uses Dilate and Vector to form points related by the same scale factor, with Segment objects to show the corresponding lengths/segments. Conditional logic (If) and Textfield are used to evaluate user input and provide feedback, while PointIn and the constructed point sets (e.g., several generated points and labeled objects) support the check against the proportional structure. Suitable for middle and high school learners, as well as for classroom demonstrations and formative assessment on ratios and linear relationships.

GeoGebra Commands & Parameters

  1. PointIn(g_1) → D
  2. Random(1, 15) → y_1
  3. Random(1, 15) → x_1
  4. Random(20, 75) → k
  5. Dilate(B, If[0 < a ≤ 1, 1 - a, 0], A) → B'
  6. Vector(B, B') → u
  7. Dilate(A, If[2 < a ≤ 3, 3 - a, 0], (0, y(D))) → A'
  8. Vector(A, A') → v
  9. Dilate(A', If[3 < a ≤ 4, 4 - a, 0], D) → C'
  10. Dilate(D, If[5 < a ≤ 6, 6 - a, 0], (x(D), y(D) + y(A'))) → D'
  11. Dilate(D', If[6 < a ≤ 7, 7 - a, 0], (x(D') + x(D), y(D'))) → E'
  12. Dilate(A, If[8 < a ≤ 9, 9 - a, 0], D) → A'_{1}
  13. Segment(A, A'_{1}) → g
  14. Dilate(D, If[9 < a ≤ 10, 10 - a, 0], E) → D'_{1}
  15. Random(-10, 10) → b_1
  16. Random(-10, 10) → n_1
  17. Random(1, 10) → d_1
  18. If(s ≥ 0, "earn", "lose") → text7
  19. If(d > 1, "hours", "hour") → text8
  20. Textfield(p) → InputBox3
  21. Textfield(o) → InputBox1
  22. If(o ≟ n_1 / d_1, "Yes!", "no") → text9
  23. If(p ≟ q, "Yes!", "no") → text10
  24. Vector(A', C') → w
  25. Dilate(D, If[9 < a ≤ 10, 10 - a, 0], E') → D'_{2}
  26. Segment(D, D'_{2}) → h
  27. Textfield(p_1) → InputBox2
  28. Textfield(q_1) → InputBox4
  29. Textfield(k_1) → InputBox5
  30. Textfield(m_1) → InputBox7
  31. Textfield(o_1) → InputBox8
  32. Textfield(l_1) → InputBox6
  33. If(c1, "√", "×") → text21
  34. If(c2, "√", "×") → text20
  35. If(c3, "√", "×") → text22

AI Drawing Prompt Reference

Create an interactive quiz on proportional relationships: start with a base geometric figure, generate several points using random parameters, then apply scaling transformations to create corresponding points, and connect them with segments to show proportional scaling. Include multiple input boxes for user answers, with check or cross marks based on comparison to expected ratios. Add sliders to control scale factors, and display dynamically generated points and segments to illustrate linear proportionality and geometric dilation.
The prompt above was compiled from the original drawing commands and is for reference only.