how can I change the Anchor point and the position of a GUI such that it will remain in the same position.
Ex
Initial AnchorPoint = 0.5, 0.5
Initial Position = 0.5, 0, 0.5, 0

Final AnchorPoint = 0, 0
Final Position = ??
and the GUI should remain in the same position on the screen

Assuming the initial anchor point is x_{a1}, y_{a1}, final anchor point is x_{a2}, y_{a2} and the initial position is x_{1}, 0, y_{1}, 0, you can get the final positionâ€™s x and y scale components like this: x = x_{1} + x_{a2} - x_{a1} y = y_{1} + y_{a2} - y_{a1}

This will give you the final position x, 0, y, 0
which will result in the same absolute position as the original situation when used with the final AnchorPoint x_{a2}, y_{a2}.