Exploring Perpendicular Bisectors (Part 1): Locating Equidistant Points

This GeoGebra example demonstrates how perpendicular bisectors help identify and visualize equidistant points relative to the endpoints of a segment, forming the foundation for finding centers and constructing circles. The key math ideas include geometry of triangles, the defining property of a perpendicular bisector (perpendicular to the segment and bisecting it), and the characterization of points that remain the same distance from two given points. In the construction, GeoGebra objects such as A_{1} and B_{1} serve as the segment endpoints (or movable triangle vertices), pic1 is used as the main visualization container/output, and the auxiliary parameter a supports adjustable configuration and dynamic updates. Suitable for secondary-school geometry, interactive construction practice, and early contest preparation focused on rigorous geometric reasoning.