Changing a rectangle

How can I change a rectangle by dragging one vertex, with (i) the rectangle remaining a rectangle, and (ii) the opposite vertex staying at the same spot?

Follow-up question:

How can I make that moving vertex coincide with and track (in animation) a vertex in another layer?

ACTUALLY (see picture), want I simply want to do is draw a rectangle with its lower left vertex at the center of the circle, and the upper right vertex following the end of the radius as it travels around the circle. The idea is that on the axis system the horizontal edge indicates the sinus, and the vertical edge indicates the cosinus.

Rectangles made with the Rectangle Tool (Alt+R) consist of two vertices
that behave exactly the way you want them to.

To have one vertex be at the same position as another one,
select both, right click on one of them and press “Link”

They now are always at the same position regardless which one you move.

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