General Rotation Transformations and Matrix Application
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This example demonstrates the dynamic process of general rotation transformations of plane figures around a fixed point. Core mathematical concepts include rotation, matrix operations, polygon properties, and angle measurement. Construction utilizes GeoGebra's ApplyMatrix command combined with Intersect, Segment, and Polygon tools to build original objects and their images, controlled by angle parameters. Suitable for high school or university geometry courses to intuitively understand linear transformations and geometric transformations, aiding teaching and learning.
GeoGebra Commands & Parameters
Intersect(xAxis, yAxis) → DSegment(D, A) → dPolygon(A, B, C) → poly1, c, a_1, b_1ApplyMatrix(M, A) → A'ApplyMatrix(M, B) → B'ApplyMatrix(M, C) → C'Polygon(A', B', C') → poly1', c', a', b'ApplyMatrix(M, D) → D'Angle(A, D, A') → αApplyMatrix(M, D) → D'_1ApplyMatrix(M, D) → D'_2Segment(D'_2, A') → h