Dilating Points: Interactive Dilation Transformation

① This GeoGebra example dynamically demonstrates the dilation (homothety) of a point A about a fixed center B with an adjustable scale factor (DilationFactor), showing the resulting image point B' and its position changes. ② The core mathematical concept is dilation (a similarity transformation), involving the scale factor, center of dilation, ratio of corresponding segment lengths (lengthAB' vs. lengthAB), and coordinate geometry relationships between points and segments. ③ Construction highlights: The Dilate command generates the dilated point B', while Line and Segment commands construct the connecting lines and segments between the center and points; multiple text objects (text1~text10) dynamically display the scale factor and segment lengths; a slider controls DilationFactor for interactive exploration. ④ Suitable for middle school to high school students learning geometric transformations, similarity, and coordinate geometry, as well as for teachers demonstrating properties of dilation such as proportional segment lengths and collinearity of points.