A path doesn't have “a position”. A path is a set of points (defined by line and curve segments). Every point has its own position. Perhaps you want to rotate the path around a particular point, instead of around the origin. The trick is to create a composite transform that combines three individual transforms: Translate the origin to the rotation point. Rotate. Invert the translation from step 1.
![Rotate CGPath without changing its position](https://cdn-ak-scissors.b.st-hatena.com/image/square/98d6f053a97a87156775f60757c60865d0f2c47d/height=288;version=1;width=512/https%3A%2F%2Fcdn.sstatic.net%2FSites%2Fstackoverflow%2FImg%2Fapple-touch-icon%402.png%3Fv%3D73d79a89bded)