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Parabola and Geometric Transformations

Parabola and Geometric Transformations
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2015-12-15 02:05
FunctionTransformationGeometric Construction
This example demonstrates the geometric properties and transformations of a parabola. It involves core mathematical concepts such as parabola, geometric transformations, and vector operations. Construction highlights include using GeoGebra commands like Point, OrthogonalLine, Angle, Line, Intersect, Segment, Vector, Translate, and Mirror. Suitable for high school and above students to learn and understand the transformation rules of function graphs.

GeoGebra Commands & Parameters

  1. Point(yAxis) → Z
  2. OrthogonalLine(Z, yAxis) → a
  3. Angle(yAxis, a) → α
  4. Point(f) → M
  5. Line(M, yAxis) → b
  6. Intersect(a, b) → M'
  7. Segment(M, M') → c
  8. Vector(B_1, C) → u
  9. Translate(M', u) → A'
  10. Mirror(A', M') → B'
  11. OrthogonalLine(A', a) → d
  12. OrthogonalLine(B', a) → e
  13. Intersect(f, d, (-3.285579521037775, 2.6987581972657035)) → A
  14. Intersect(f, e, (0.714420478962225, 0.12759915519015377)) → B
  15. Segment(A, A') → g
  16. Segment(B, B') → h
  17. Segment(B, A) → i
  18. Line(M, i) → j

AI Drawing Prompt Reference

Please draw a figure that includes a parabola and geometric transformations. First, select a point on the y-axis and draw its vertical line. Then, choose a point on the parabola and connect it to the y-axis. Find the intersection of these two lines and draw a segment connecting the original point with this intersection. Next, perform vector operations and translations by moving the intersection along a certain vector to get a new point, then mirror this new point. Finally, draw vertical lines from these points and find their intersections with the parabola, connecting relevant points to form segments and lines.
The prompt above was compiled from the original drawing commands and is for reference only.