3 Transformation Applications

Here are some real-world applications of geometric transformations. Can you think of others?

1. Translations
   • Escalators: The steps move in a straight-line translation while maintaining their shape and size.
   • Animation: Characters move across the screen using translations in computer graphics.
2. Rotations
   • Windmills and Ferris Wheels: These structures rotate around a fixed point.
   • Car Tires: When a car moves, its wheels rotate around their center.
3. Reflections
   • Mirrors and Water Reflections: Objects appear as flipped versions in reflective surfaces.
   • Symmetry in Architecture: Buildings often have symmetrical reflections, like in Gothic cathedrals.
4. Points, Lines, and Planes
   • Navigation Systems: GPS relies on mapping points, lines (roads), and planes (land surfaces).
   • Engineering and Drafting: Blueprints use points, lines, and planes to create structures.
5. Angles
   • Construction and Carpentry: Proper angles ensure stability in buildings, furniture, and bridges.
   • Sports: The angle of a soccer kick or basketball shot determines trajectory and success.
6. Simple Curves
   • Highway and Railroad Design: Roads and tracks use curves to ensure smooth and safe travel.
   • Roller Coasters: Curved paths make rides more exciting and prevent abrupt changes in motion.