Trying to use the Rotate Tool to move a rectangle AROUND a circle.
Instead both the rectangle and circle rotate.
How do I stop this from moving? The circle should be fixed in its position.
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The cause of problem is Handle
It seems you didn't centralized your Rotation handle therefore it will rotate around Axes of current handle basically when you merge paths or group paths handle doesn't stay in perfect center and it changes to center of bound so before rotating make sure you allign your Handle to center :) Hope it helps!
You could use the Transform Effect.
Simple extend the rectangle so the bottom of it is flush with the center of the circle.
Select only the rectangle and choose
Effect > Distort & Transform > Transform
In the Transform dialog window, tick the bottom center for the origin point (and tick "preview") and then rotate all you want.
You can then leave the effect as a live effect which you can adjust later if needed.
Or you can choose
Object > Expand Appearance to "bake in" the rotation.
You can also use the Transform Panel and
Again extend the rectangle so the bottom is flush with the center of the circle. Set the origin point on the Transform Panel to the bottom center and enter a value in the rotate field and tap Return/Enter. If the rotation is incorrect,
Edit > Undo and try again.
You can only enter 1 rotation step and then you need to
Undo because after each rotation the bottom center origin is different based upon the last rotation.
I find these methods work better for me. I dislike trying to hunt and peck for the exact center of things with the rotate tool. Smart Guides make it easier, but using the Effect allows me to alter later if I want. Unless they've altered things in the last release, the Rotate Tool won't honor the 9-point origin setting.