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Absolute Value Equation Illustrator

Absolute Value Equation Illustrator
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2016-11-18 06:10
FunctionInequalityGeometric ConstructionSlider AnimationGraphing
In collections A1.ACE.1 - Create and solve equations and inequalities Absolute Value Equations & Inequalities Absolute Value Equations & Inequalities
This interactive GeoGebra example dynamically illustrates absolute value equations (such as |x-a|+|x-b|=c) by showing their geometric meaning and how solutions change with adjustable parameters. The core mathematical concepts include absolute value, distance, equation solving, and geometric representation on the number line. Construction highlights: using GeoGebra commands such as Ray, Point, Mirror, Vector, Distance, Segment, Circle, Intersect, Polygon, and Dilate, the applet builds objects like a, A, B, C, f, g, E, E', u, v, and displays distances AE and AE' with text labels. Sliders and buttons allow real-time parameter adjustment. This resource is suitable for middle and high school students learning absolute value equations and distance concepts, as well as for teachers demonstrating dynamic geometry in class. It emphasizes visualization and interactivity to connect algebraic solutions with geometric distances.

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

AI Drawing Prompt Reference

Draw a geometric representation of an absolute value equation, including two rays f and g starting from point A and pointing to points B and C respectively. Point E is on ray f, and point E' is the mirror image of E with respect to point A. Draw vectors u and v from point A to points E and E' respectively. Show the distances AE and AE'. Use circles and central symmetry transformations to construct several circles and segments, illustrating distance relationships. Finally, use sliders to adjust parameters and dynamically show changes in the equation's solutions.
The prompt above was compiled from the original drawing commands and is for reference only.