- #1
kingwinner
- 1,270
- 0
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!
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!