Dilation of a Line

This GeoGebra example demonstrates the dilation (scaling) of a line. It shows how a line is transformed by applying a dilation centered at a point (likely the origin) with a scale factor, mapping points on the original line to new positions, resulting in a new line that is parallel to the original (or coincident if the scale factor is 1). The core mathematical concept is dilation, a similarity transformation that preserves the shape of geometric objects but changes their size and position. The construction uses GeoGebra commands: Line to create the original line f, Ray to construct auxiliary rays, and Dilate to scale key points A and B to their images A' and B', which are then connected to form the dilated line i. Additional objects (C, g, h, k) are included, possibly to control the scale factor or visualize the transformation process. This example is suitable for middle school geometry or college analytic geometry courses, helping students understand how dilation affects a line and the relationship between the original and transformed line equations.