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Reflection in a Vertical Mirror

Reflection in a Vertical Mirror
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2016-08-30 10:06
VectorCoordinate GeometryTransformationGeometric Construction
This example demonstrates the reflection of an object in a vertical mirror. It involves core mathematical concepts such as reflection, vectors, coordinate geometry, and geometric construction. Key GeoGebra commands and objects used in the construction include Segment, Midpoint, Vector, If, and Textfield. It is suitable for high school students learning coordinate geometry and transformations.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Midpoint(G, H) → I
  3. Midpoint(E, C) → J
  4. Midpoint(J, D) → L
  5. Midpoint(D, I) → T
  6. Midpoint(R, S) → U
  7. Vector(J, K) → v
  8. Vector(K, D) → u
  9. Vector(Q, D) → a
  10. Vector(I, Q) → b
  11. Vector(M, K) → w
  12. Vector(U, Q) → c
  13. If(y(Q) < y(B), 0, 1) → BottomCheck1
  14. If(y(Q) > y(A), 0, 1) → BottomCheck2
  15. If(y(K) > y(A), 0, 1) → TopCheck1
  16. If(y(K) < y(B), 0, 1) → TopCheck2
  17. Vector(A, D) → l
  18. Vector(B, D) → n
  19. Segment(N, O) → p
  20. Segment(V, W) → q
  21. Vector(Z, A) → k
  22. Segment(A_1, B_1) → r
  23. Segment(D_1, C_1) → s
  24. Vector(E_1, A) → t
  25. Vector(O_1, B) → m
  26. Vector(R_1, B) → u_1
  27. Textfield(h) → InputBox1
  28. Textfield(size) → InputBox3
  29. Textfield(height) → InputBox4
  30. Textfield(position) → InputBox2
  31. Segment(J_1, K_1) → f_1
  32. Segment(L_1, M_1) → g_1
  33. Vector(U_1, J) → h_1
  34. Vector(W_1, D) → i_1
  35. Vector(B_2, A) → v_1
  36. Vector(C_2, B) → w_1

AI Drawing Prompt Reference

Draw a diagram showing reflection in a vertical mirror. Start with a vertical mirror line. Place an object on the left side of the mirror, marked by several key points. From these points, draw vectors indicating the direction and position before and after reflection. Construct the reflected object on the right side, making it symmetric to the left about the mirror. Add several input boxes for parameters like height, size, and position. Include conditional checks to control the display of the object within the mirror's vertical range. Finally, connect relevant points with segments to complete the reflection construction.
The prompt above was compiled from the original drawing commands and is for reference only.