Hide/Show Moveable Point?

I’m creating a task where students use a “protractor”. I have a PNG and am using a moveable point for students to place the protractor. However, I want to be able to toggle show/hide the protractor (and other aspects of the graph) by using the Multi-Select.

I know you can add a something like P=(a, b {p=1}) , but it ends up limiting the moveability to horizontal only. Suggestions??

Annnnnd, just figured out a workaround for my own problem to hide/show the image, although the moveable point doesn’t hide.

Added a variable multiplier to the width and height of the image:

Width: 10p
Height: 8p

and changed p=0 or p=1 based on whether option is checked or not in Multi-Select.