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Image of a Point Reflected by a Sphere

Image of a Point Reflected by a Sphere
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2016-10-05 14:48
Solid GeometryTransformationGeometric Construction
This example demonstrates the image of a point reflected by a sphere. Key mathematical concepts include reflection transformation and spherical geometry. The Surface command is used to construct the sphere S, reflection line L, reflection plane n, reflection line l, and reflected sphere L_S. Suitable for high school geometry and solid geometry courses.

GeoGebra Commands & Parameters

  1. Surface(((cos(u) * sin(v)), (sin(u) * sin(v)), cos(v)), u, 0, π, v, 0, (2 * π)) → S
  2. Surface(S(u, v), u, 0, π, v, 0, (2 * π)) → n
  3. Surface((x(L) - ((2 * l(u, v)) * x(n(u, v))), y(L) - ((2 * l(u, v)) * y(n(u, v))), z(L) - ((2 * l(u, v)) * z(n(u, v)))), u, 0, π, v, 0, (2 * π)) → L_S