Reflection about the line y=x

This example demonstrates the reflection (mirror) transformation of a polygon (triangle) about the line y=x, visually showing the positional relationship between the original and reflected figures. The core mathematical concept is reflection (axial symmetry) in the plane, involving matrix representation, vector operations, and the coordinate-swapping rule (point (x,y) maps to (y,x)). Construction highlights: using GeoGebra's Polygon command to construct triangle poly1, then applying a reflection tool or matrix transformation to generate its image; the construction summary mentions objects f (possibly the reflection function or line), A, B, C (triangle vertices), poly1 (original polygon), c (possibly a circumcircle), a, b (sides or auxiliary objects), integrating polygons, circles, and vectors. Suitable for upper middle school to high school students to understand the geometric meaning and algebraic expression of axial symmetry, and also serves as a visual aid for teaching matrix transformations.