Geometric transformations involve moving figures from one location to another without altering their size or orientation. A fundamental example involves shifting a figure across a coordinate plane. The original figure, the pre-image, is moved a specified number of units horizontally and vertically to create a new figure, the image. For example, a triangle with vertices at (1, 1), (2, 3), and (4, 1) could be shifted 3 units to the right and 2 units up, resulting in a new triangle with vertices at (4, 3), (5, 5), and (7, 3).
Understanding this process is crucial in several fields. In computer graphics, it underpins the rendering of 2D and 3D objects and animations. In architecture and engineering, it allows for the precise positioning of structural elements and components in designs and blueprints. Historically, the principles behind this process were implicitly understood by artisans and craftspeople, but the formalization using coordinate systems allowed for a more rigorous and quantifiable approach. Its significance lies in its ability to provide a clear and precise method for relocating figures, ensuring accuracy and predictability.
