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Reflection in Coordinate Plane

Reflection in Coordinate Plane
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2018-03-25 22:48
Coordinate GeometryGeometric Construction
This example demonstrates the reflection of points, line segments, and polygons in the coordinate plane. It involves core math concepts like coordinate transformation, symmetry, and analytical geometry. Constructed using commands and objects such as Mirror, Textfield, SelectedIndex, Line, Segment, Midpoint, Length, OrthogonalLine for dynamic reflection operations. Suitable for high school students learning geometric transformations and their coordinate representations.

GeoGebra Commands & Parameters

  1. Mirror(A, xAxis) → A_x
  2. Mirror(A, yAxis) → A_y
  3. Textfield(p) → InputBox1
  4. Textfield(q) → InputBox2
  5. SelectedIndex(VoH) → i
  6. Line(B, yAxis) → f
  7. Line(B, xAxis) → g
  8. Mirror(A, f) → A_bv
  9. Mirror(A, g) → A_bh
  10. Segment(A, P) → j
  11. Segment(A_y, P) → l
  12. Segment(C, A) → m
  13. Segment(C, A_x) → n
  14. Midpoint(m) → D
  15. Midpoint(n) → E
  16. Length(m) → c
  17. Length(n) → d
  18. OrthogonalLine(A, g) → r
  19. Segment(A, P_2) → s
  20. Segment(P_2, A_bv) → t
  21. Segment(A, P_1) → e
  22. Segment(P_1, A_bh) → f_1
  23. Midpoint(e) → F
  24. Midpoint(f_1) → G
  25. Midpoint(s) → H
  26. Midpoint(t) → I
  27. Length(e) → o
  28. Length(s) → u

AI Drawing Prompt Reference

Draw reflected figures of points, line segments, and polygons in a coordinate plane to demonstrate symmetry across the x-axis and y-axis. Start by marking input points, then reflect them across the axes, connect original and reflected points with line segments, and calculate lengths and midpoints. Finally, draw perpendicular lines and show reflections of line segments across these lines to illustrate the dynamic process of geometric transformations.
The prompt above was compiled from the original drawing commands and is for reference only.