I think it would be very helpful if, in the next version of Scratch, one could set multiple costume centers, one that would be the point on which the sprite rotates, the other the point where other sprites go when one uses a "go to___" block.
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It would be useful to have multiple centers, but it would probably be complicated.
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It is possible to make this with trigonometry, but it's quite complicated. As per your suggestion, I think it'd be a bit strange and confusing, especially for new users, when they find that their sprites rotate around a different point than they move.
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