Geometric Distance Representation of Absolute Value

This example demonstrates how absolute value can be visualized geometrically by tracking how distances from a point to reference objects (and their mirrored counterparts) change, emphasizing that absolute value measures magnitude without direction. It centers on the definition and geometric meaning of absolute value, the use of distance in the plane, and symmetry via mirror constructions. The construction uses GeoGebra commands and objects such as Ray and Point to set up the geometric framework, Mirror to create corresponding mirrored points, Vector and Segment to model directions and segments, Distance to compute the relevant magnitudes, Circle plus Intersect to locate key intersection points, and TextAE/TextAE' to display the distance-to-value relationships. It further employs Polygon and Dilate for structured visualization and interpretation. Suitable for middle to high school math lessons on algebra and coordinate/geometry connections, especially for introducing absolute value through dynamic geometry.