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Mirror Transformation of a Sphere

Mirror Transformation of a Sphere
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2015-05-23 09:04
VectorSolid GeometryTransformationGeometric Construction
This example demonstrates how to perform mirror transformation of a sphere using GeoGebra. Key mathematical concepts include spheres, vectors, and geometric transformations. Using commands like Mirror, Circle, Point, Sphere, Segment, and Angle, the construction of the sphere's mirror image is achieved. Suitable for high school mathematics education and learning about solid geometry transformations.

GeoGebra Commands & Parameters

  1. Mirror(A, B) → A'
  2. Circle(A', C, A) → c
  3. Point(zAxis) → D
  4. Sphere(D, A') → a
  5. Segment(D, B) → b
  6. Angle(D, B, C) → α
  7. Segment(B, C) → d
  8. Corner(1, 5) → E

AI Drawing Prompt Reference

Draw the mirror image of a sphere. First, create point A and point B, then create a mirrored point A' through A and B. Next, draw a circle c with A' as the center and C as the radius. Then, create point D on the z-axis, and draw a sphere a with D as the center and A' as the radius. Draw a line segment b from D to B, and an angle α from D to B to C. Finally, draw a line segment d from B to C to define the mirror angle.
The prompt above was compiled from the original drawing commands and is for reference only.