A quick question this time... Example: Let (u,v)=f(x,y)=(x-2y, 2x-y). Find the region in the xy-plane that is mapped to the triangle with vertices (0,0),(-1,2),(2,1) in the uv-plane. Solution: (0,0)=f(0,0), (-1,2) = f(5/3,4/3), and (2,1)=f(0,-1), the region is the triangle with these vertices. My question is: Yes, we get three points, but how do you know FOR SURE that the region is a TRIANGLE? I am lost here... Thanks for explaining!