Geometric transformations alter the position or size of a figure. These include mirroring across a line, shifting a figure without changing its orientation, turning a figure around a fixed point, and scaling a figure proportionally from a center point. Consider a triangle on a coordinate plane. Reflecting it over the x-axis produces a mirror image. Translating it moves it a certain number of units left or right, and up or down. Rotating it about the origin changes its orientation. Finally, dilating it either enlarges or reduces its size, keeping the same shape.
These transformations are fundamental in various fields. In computer graphics, they are essential for creating animations and manipulating objects in virtual environments. In architecture and design, they provide tools for creating symmetrical patterns and adjusting scales. Historically, the study of these operations dates back to ancient geometry, with their applications evolving alongside advancements in mathematics and technology. Their consistent properties, like preserving angles in all but one operation, make them invaluable for analyzing and understanding geometric relationships.
