I think I vaguely remember the controversy, but pending Baner's posting of links, I am going to post something for you to critique.
The region R "usually" should be a closed region, but that's not necessary. A region represents a set of points, and in this case, for example, its a straight line.
Now (1) doesnt tell us about the point (r,s). It gives a relationship between r, s and that is a line. So all points lying on that line could be the points r,s. The current case would be easy, since the equation of the line defining (r,s) doesn't coincide with the region defined. So they would intersect at one point, and unless you know the actual values of r,s you cannot tell if the point rs would lie in the region ( = on the line).
Therefore (1) is insufficent.
(2) Clearly defines the point, which makes it easy to figure out if the point r,s lies on the line (in the region) or not. Thus sufficient.
Who says elephants can't dance?