Translations: Vector-Based Shifting of Triangles and Logarithmic Graphs

This GeoGebra example demonstrates how a triangle, its circumcircle, and a logarithmic function graph are translated by a given vector, visually showing that translation preserves shape and size. The core mathematical concepts include translation as a similarity transformation, vectors, polygons, circles, logarithmic functions, and right triangles. Construction highlights: the Polygon command creates triangle poly1, the Vector command defines translation vector u, and the Translate command shifts the triangle, circle, and function graphs to produce images poly1', c', a', and b'. The Distance command measures distances between corresponding points to verify the isometric property. This resource is suitable for middle and high school students learning geometric transformations, vectors, and function graph shifts, and for teachers demonstrating the coordinate changes underlying translation.