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Absolute Value Inequality Demonstrations

Absolute Value Inequality Demonstrations
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2016-11-20 09:18
FunctionCoordinate GeometryInequality
This example demonstrates absolute value inequalities dynamically. Key mathematical concepts include absolute values and inequalities. Using GeoGebra commands such as Ray, Point, Distance, etc., the solution set of the inequality can be dynamically shown. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Ray(A, B) → f
  2. Ray(A, C) → g
  3. Point(f) → E
  4. Mirror(E, A) → E'
  5. Vector(A, E) → u
  6. Vector(A, E') → v
  7. Distance(A, E) → distanceAE
  8. Distance(A, E') → distanceAE'
  9. Ray(F, H) → h
  10. Ray(D, G) → l
  11. Segment(D, F) → m
  12. Circle(A, 1) → c
  13. Circle(E', 1) → d
  14. Circle(E, 1) → e
  15. Circle(D, 4) → c_1
  16. Circle(F, 4) → d_1
  17. Intersect(c_1, t, 1) → L
  18. Intersect(d_1, t, 1) → M
  19. Segment(D, L) → f_1
  20. Segment(F, M) → g_1
  21. Polygon(O, N, 4) → poly1, h_1, i_1, j_1, k_1, R, S
  22. Polygon(Q, P, 4) → poly2, l_1, m_1, n_1, p_1, T, U
  23. Distance(S, R) → distanceSR
  24. Distance(U, T) → distanceUT
  25. Dilate(A, If[0 < b ≤ 1, 1 - b, 0], E) → A'
  26. Segment(A, A') → q_1
  27. Dilate(A, If[0 < b ≤ 1, 1 - b, 0], E') → A'_1
  28. Segment(A, A'_1) → r_1
  29. Dilate(F, If[1 < b ≤ 2, 2 - b, 0], M) → F'
  30. Dilate(D, If[1 < b ≤ 2, 2 - b, 0], L) → D'
  31. Segment(F, F') → p
  32. Segment(D, D') → q
  33. Translate(poly1, (-1.5, 0)) → poly1'
  34. Translate(poly2, (1.5, 0)) → poly2'
  35. Distance(U, T) → e_1
  36. Distance(S, R) → o_1

AI Drawing Prompt Reference

Draw a dynamic graph of absolute value inequalities. First, draw two rays f and g, then take point E on ray f and reflect it to E' with respect to point A. Draw vectors u and v, and calculate the distances of AE and AE'. Next, draw rays h and l, and line segment m, then draw circles c, d, and e with radius 1, and circles c_1 and d_1 with radius 4. Find the intersection points L and M of circles c_1 and d_1 with line t, draw line segments f_1 and g_1, then draw polygons poly1 and poly2, and their translations poly1' and poly2', and finally draw line segments q_1, r_1, p, and q, and adjust the size and position of the polygons.
The prompt above was compiled from the original drawing commands and is for reference only.