The problem is: R is the parallelogram bounded by the lines x+y=2, x+y=4, 2x-y=1, and 2x-y=4. Use the transformation u=x+y and v=2x-y to find the area of R. I am not sure how to complete this problem. My first issue is that I don't know how to convert the transformation functions into functions of u and v, to find the Jacobian. Second, the region R is a diamond shape in the xy plane. I don't understand how to map this figure into the uv plane. Could someone please provide some advice on this problem? Thanks for your help.