Clockwise Rotation Construction: Angles and Segment Mapping

This example demonstrates how to perform a clockwise rotation in the plane for a given segment/point using a specified rotation angle, and how to relate the pre- and post-rotation positions. The main mathematical ideas include geometric transformations (Rotation), measuring/using an Angle as the rotation parameter, constructing segments (Segment), and verifying the invariance of key lengths via Distance. Construction approach in GeoGebra: create the required line segments with Segment; apply Rotate around a center point C with an angle (α or β) to generate the rotated images such as the corresponding point B'; then use Distance to check that relevant distances/lengths are preserved under the rotation. The construction objects referenced in the command summary—C, α, B, f, B', g, a, pic1, pic1', and β—represent the rotation center, angle parameters, original points/segments, and their rotated counterparts. Suitable for middle school to early high school geometry instruction and for lessons on transformation geometry and interactive geometric constructions.