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Reflection about x=0

Reflection about x=0
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2020-09-29 22:12
Coordinate GeometryTransformationGeometric Construction
In collections Reflecting about Planes
This example demonstrates reflecting objects about the x=0 axis. Key mathematical concepts include reflection transformation and coordinate geometry. Using GeoGebra commands such as Plane, Mirror, Line, Intersect, etc., the reflection can be constructed. Suitable for students at middle school level and above to learn about reflection transformations and coordinate geometry.

GeoGebra Commands & Parameters

  1. Plane(A, B, C) → p
  2. Mirror(O, p) → O'
  3. Line(O, O') → f
  4. Intersect(p, f) → D
  5. OrthogonalLine(D, Vector[D, O], Vector[D, B]) → j
  6. Plane(f, j) → q
  7. Dilate(O, If[0 < SlideMe ≤ 1, 1 - SlideMe, 0], D) → O'_{1}
  8. Segment(O, O'_{1}) → g
  9. Dilate(D, If[1 < SlideMe ≤ 2, 2 - SlideMe, 0], O') → D'
  10. Segment(D, D') → h
  11. OrthogonalLine(D, Vector[O, O'], xOyPlane) → i
  12. Point(i) → E
  13. Rotate(O, If[2 < SlideMe ≤ 3, ((SlideMe - 2) * π), π], D, q) → O'_{2}
  14. Rotate(O'_{1}, If[2 < SlideMe ≤ 3, ((SlideMe - 2) * π), π], D, q) → F
  15. Segment(O'_{2}, F) → g'
  16. Point(j) → G
  17. Angle(G, D, O) → α

AI Drawing Prompt Reference

Draw a reflection graph about the y-axis in a plane. Start with point O and its reflection O' on the y-axis, forming a line f. Line f intersects the original figure at point D. From point D, draw a perpendicular line j to the y-axis and construct a new plane q using f and j. In plane q, dilate points O and D to get O'_{1} and D'. Connect O'_{1} and D', and draw perpendiculars from D to the y-axis and the original figure to get point E. Then, rotate points O and O'_{1} in plane q to get O'_{2} and F. Connect O'_{2} and F, and calculate the angle α between points G, D, and O.
The prompt above was compiled from the original drawing commands and is for reference only.