Geometric Transformation: Resizing and Dilating Figures

This applet demonstrates geometric dilation and scaling transformations in plane geometry. Using GeoGebra's built-in Dilate command, users can explore how polygons such as triangles, quadrilaterals, and trapezoids change in size while preserving their shape when transformed relative to a specified center of dilation. The applet allows students to interactively adjust the scale factor and reposition the center of dilation, observing in real time how every point of the original figure maps to a corresponding point on the transformed figure along rays originating from the center. Key features include the display of corresponding vertices connected by construction lines, measurements of side lengths before and after the transformation, and angle comparisons that remain invariant under dilation. These visual and numerical aids help learners discover that dilations preserve angle measures and produce proportional side lengths, which are the defining properties of similar figures. The applet also highlights the distinction between congruent transformations, which preserve both size and shape, and dilations, which preserve shape but scale size by the given factor. Additionally, the concept of homothety is introduced as the formal geometric term for dilation, emphasizing the role of the center point and scale ratio. By manipulating the slider for the scale factor, students can observe what happens when the factor is greater than one, between zero and one, exactly one, or negative, gaining insight into enlargement, reduction, identity, and reflection scenarios. This hands-on exploration supports the development of intuitive understanding of core geometry topics including similarity, proportionality, and geometric transformations, making abstract definitions tangible and reinforcing connections between algebraic ratios and visual spatial reasoning.