Take the line segment whose endpoints are the points (1,0) and (-1,0) and a point of rotation (x,y).

If the segment is rotated all the way around the point it will trace out an annulus.

Find simplified formula for the area of this annulus in terms of x and y.

Redo this problem for a rectangle with corners at (1,1), (-1,1), (-1,-1), and (1,-1).

(In reply to re: part 1 not finished. by broll)

The annulus is defined by the segment not its endpoints.  Sometimes the boundaries of the annulus are the endpoints and sometimes they are not.

If the origin (or any point of the segment) is selected the segment sweeps out a circle, which is just an annulus with an inner radius of zero.  Your formula gives zero but we clearly have a positive area, so the problem is with the formula.

Posted by Jer on 2010-12-21 15:08:01