Dilations of Triangles with Movable Center

① This example demonstrates how to dilate a triangle and allows the user to move the center of dilation, visually exploring the relationship between the original triangle and its image. ② The core mathematical concept is dilation (a similarity transformation), involving similar triangles, scale factor, and the property that corresponding points lie on rays from the center with distances proportional to the scale factor. ③ Construction details: Using GeoGebra commands such as Segment, Polygon, Ray, Circle, and Intersect, the original triangle, dilation center, scale factor slider, and the dilated triangle are constructed; rays from the center through each vertex are used to locate the image vertices via intersection points, and corresponding polygons and text labels are generated. ④ Suitable for upper middle school or high school geometry classes to study similarity transformations, the role of the dilation center and scale factor, and as an interactive exploration tool in dynamic geometry environments.