Geometric Insight into Absolute Value: Visualizing |a| with Construction

This GeoGebra example demonstrates how the absolute value of a number can be represented geometrically as a distance/position on the plane, making the non-negative and sign-symmetric behavior of |a| visible as parameters change. The key math ideas include the definition of absolute value, the role of sign (positive/negative), integer-based arithmetic operations, and interpreting numeric magnitude through geometric measurements. Construction highlights: it uses If to branch between cases depending on the sign/region; Random to generate different test inputs; Point, Midpoint, and Circle to create reference points, midpoints, and circular relationships; and Rotate to apply transformations that reposition objects consistently with the absolute-value rule. It also uses parameter bounds (xmin/xmax) and annotation objects (e.g., multiple text labels and picture groups such as pic1/pic2/pic3) to present comparisons and dynamic updates (including variables like d and d′, and animated step control such as jump). Suitable for middle/high school teaching, especially for introducing absolute value and supporting interactive exploration that links algebraic meaning to geometric interpretation.