Parabola Construction: Locus via Right Triangles and Perpendicular Bisectors

This example demonstrates how to construct a parabola through geometric construction, using right triangles and perpendicular bisectors to generate the locus of a moving point. The core mathematical concept is the definition of a parabola as the set of points equidistant from a fixed point (focus) and a fixed line (directrix). The construction steps involve creating lines and points with the Line and Point commands, building perpendicular bisectors with LineBisector, drawing perpendicular lines with OrthogonalLine, finding intersections via Intersect, and finally using the Locus command to trace the parabola. This activity is suitable for upper middle school or high school students, helping them grasp the geometric nature of conic sections and the power of dynamic geometry software in exploring loci and constructions.