Slider Exercise 2: Combined Midpoint, Rotation and Dilation Transformations

① This example demonstrates dynamic geometric transformations controlled by sliders, combining midpoint, rotation, and dilation (homothety) effects, with connections to hyperbola and logarithmic functions. ② Core mathematical concepts include midpoint, dilation, rotation, median line, hyperbola, logarithm, and stochastic processes, highlighting the interplay between transformation geometry and function graphs. ③ Construction details: GeoGebra commands used are Midpoint, Dilate, Segment, and Rotate; objects include points A, B, C and their transformed images A', C', A'', lines f and g, and function f', all driven by slider a for dynamic variation. ④ Suitable for high school or early college students to understand composition of geometric transformations, parametric dynamic visualization, and to explore how transformations affect function graphs; also useful for teachers creating interactive instructional materials.