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Absolute Value Inequalities Demo

Absolute Value Inequalities Demo
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2019-09-03 06:39
TrigonometryOptimizationInequalityGeometric ConstructionGraphing
This example demonstrates the geometric interpretation and solution set representation of absolute value inequalities. It involves core math concepts like absolute value, inequality solving, and geometric visualization. Construction highlights include commands/objects such as Ray, Point, Mirror, Vector, Distance, Segment, Circle, Intersect, Polygon, Dilate, Translate in GeoGebra. Suitable for high school mathematics teaching and learning, helping to understand the graphical solution method for absolute value inequalities.

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 two rays starting from one point and passing through two other points. Locate two points on these rays and draw circles centered at these points. Also, draw a circle centered at another point with radius 1, and two circles with radius 4. Find the intersections of these circles and connect the corresponding points to form segments. Finally, perform scaling and translation operations based on specific conditions to obtain the final figure.
The prompt above was compiled from the original drawing commands and is for reference only.