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In real life a transformation is a complete change, an overhaul that forever improves something, a person, a device. In Illustrator a transformation is very nearly the opposite, much less grand, much more common, definitely not an overhaul. A transformation is any operation that changes a path without affecting its original structure. After transforming a path its points in segments remain basically in the same position relative to each other as they were before. An example is scaling. If you enlarge a five- pointed star, it's still a five-pointed star, it's just bigger.
Rotation is a transformation. So are or reflecting and slanting. Those are the main four, but you could argue there are others as well. Offsetting a path moves all the points outward or inward. The Reshape Tool often adds points, but the stretched shape remains recognizable, and the simple act of moving a path is a transformation. But while transformations are hardly transformative, they are undeniably powerful. They permit you to size paths to match each other. You can repurpose paths and build ambitious illustrations and with a few seconds work you can transform and duplicate paths to create symmetrical shape sequences that would take minutes or even hours to render with traditional tools. So the transform tools. They don't really transform paths.
They transform whole illustrations.
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