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Hyperbola and Geometric Transformations

Hyperbola and Geometric Transformations
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2017-07-11 17:41
Coordinate Geometry
This example demonstrates the geometric properties and symmetry of hyperbolas. It involves core math concepts like hyperbolas, geometric transformations, polynomial functions, and histograms. Construction highlights include using commands such as Polygon, RotateText, Textfield, Sequence, and TableText to create polygons, texts, sequences, and tables. Suitable for high school mathematics teaching to understand analytical geometry and function graphs.

GeoGebra Commands & Parameters

  1. Polygon((0, 0), (0, 150), (10, 150), (10, 0)) → poly1, f, g, h, i
  2. RotateText("weight (kgs)", 90°) → text3
  3. Textfield(step) → InputBox1
  4. Textfield(first_1) → InputBox2
  5. Textfield(change) → InputBox3
  6. Sequence((i, first_1 + (change * i)), i, 0, 10) → list1
  7. Sequence(Segment[(i, (change * i) + first_1), (i + 1, (change * i) + first_1)], i, 0, 9) → list2
  8. Sequence(Segment[(i + 1, (change * i) + first_1), (i + 1, (change * (i + 1)) + first_1)], i, 0, 9) → list3
  9. Textfield(first) → InputBox4
  10. Textfield(change1) → InputBox5
  11. Textfield(change2) → InputBox6
  12. Sequence(change1 + (change2 * (i - 1)), i, 1, 10) → list5
  13. Sequence(first + change1 + (change2 * (i - 1)) + (change2 * i), i, 0, 10) → list6
  14. TableText({{sn, w_1, c_1}, {1, first_1 + change, change}, {2, first_1 + (change * 2), change}, {3, first_1 + (change * 3), change}, {4, first_1 + (change * 4), change}, {5, first_1 + (change * 5), change}, {6, first_1 + (change * 6), change}, {7, first_1 + (change * 7), change}, {8, first_1 + (change * 8), change}, {9, first_1 + (change * 9), change}, {10, first_1 + (change * 10), change}}, "|_r") → text6
  15. TableText({{sn, w_1, c_1, c_2}, {A2, B2, C2, D2}, {A3, B3, C3, D3}, {A4, B4, C4, D4}, {A5, B5, C5, D5}, {A6, B6, C6, D6}, {A7, B7, C7, D7}, {A8, B8, C8, D8}, {A9, B9, C9, D9}}, "|_r") → text5

AI Drawing Prompt Reference

Draw a hyperbola in the coordinate system and perform geometric transformations around it. First, draw a rectangle, then create a rotated text label indicating weight. Next, input starting and changing values to generate a series of points and line segments, forming a tilted line. Finally, create a table listing these point sequences.
The prompt above was compiled from the original drawing commands and is for reference only.