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Reflections over x and y axes

Reflections over x and y axes
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2018-02-02 00:51
Coordinate GeometryTransformationGeometric Construction
This example demonstrates the reflection transformation of points, line segments, and polygons over the x-axis and y-axis. It involves core mathematical concepts such as coordinate transformation, symmetry, and analytical geometry. The construction uses GeoGebra commands and objects like Polygon, Join, Point, Segment, and Mirror. Suitable for high school students learning analytical geometry and geometric transformations.

GeoGebra Commands & Parameters

  1. Polygon((-10, 6.4), (25, 6.4), (25, 10), (-10, 10)) → TopBox, f, g, h, i
  2. Join(Sequence[Sequence[(i, j), i, -7, maxx, 1], j, miny, 6, 1]) → GridSpace
  3. Polygon((7.4, 8), (25, 8), (25, -8), (7.4, -8)) → RightBox, j, k, l, m
  4. Point(GridSpace) → A
  5. Point(GridSpace) → B
  6. Point(GridSpace) → C
  7. Segment(A, B) → AB
  8. Segment(B, C) → BC
  9. Segment(C, A) → CA
  10. Mirror(A, x = 0) → A'
  11. Mirror(B, x = 0) → B'
  12. Mirror(C, x = 0) → C'
  13. Mirror(A, y = 0) → A'_1
  14. Mirror(B, y = 0) → B'_1
  15. Mirror(C, y = 0) → C'_1
  16. Segment(A', B') → AB'
  17. Segment(B', C') → BC'
  18. Segment(C', A') → CA'
  19. Segment(A'_1, B'_1) → AB'_1
  20. Segment(B'_1, C'_1) → BC'_1
  21. Segment(C'_1, A'_1) → CA'_1
  22. Segment((0, -6.4), (0, 6.4)) → Yaxis
  23. Segment((-7.4, 0), (7.4, 0)) → Xaxis
  24. Segment((0, 6.3), (0, -7)) → yaxis

AI Drawing Prompt Reference

Draw a grid composed of rectangles and triangles, with three random points placed on it, connected to form a triangle. Then, reflect these three points across the x-axis and y-axis to get three sets of new points, and connect them to form three new triangles. Finally, add the x-axis and y-axis as reference lines.
The prompt above was compiled from the original drawing commands and is for reference only.