A parallelogram P in the $xy$-plane has vertex $(0,0)$, $(2, 10)$, $(3, 17)$, and
$(1, 7)$.
I need to find a linear transformation that maps P onto a rectangle $R$ in the $uv$-plane with opposite vertices $(0,0)$ and $(4,2)$ in order to calculate a related integral.
I can't seem to find a correct linear transformation. What could I try? Is there a procedure that can be applied in this sort of scenarios?
Best Answer
Hint: Since you have common vertices $(0,0)$, it all boils down to transforming the side vectors extending from $(0,0)$ from one quadrilateral to the other. This can easily be done with elementary matrix operation construction. Let me know if you'd like me to spell it out more fully and I'll be happy to do so.