Match Point Problem: Construction and Verification on Complex Plane

This GeoGebra example demonstrates the geometric solution of a match point problem on the complex plane. Using z1, z2, and z3 as known complex points, the construction employs the Segment command to create auxiliary lines, combined with circumcircle properties and median line concepts to find matching points satisfying specific conditions. The core mathematical concepts involved include complex number representation, conic section properties, and point coordinate transformations. Construction details: Using Segment command to generate line segments, defining conic equations through objects like eq1, f, g, and h, ultimately verifying whether the match point lies on the circle. Suitable for high school mathematics extension courses, complex number geometry studies, or university-level preparatory mathematics.