Solving Geometric Transformations

Question

I am trying to understand my notes on geometric image transformations.

-"A pixel at coordinate (x,y) in the original image moves to the location ((2x+y)/3, x) in the new image.

The pixel is now at (y, 3x-2y)."

I'm really confused how (2x+y)/3 becomes 3x-2y. Can someone please point me in the right direction?

Please let me know if I've left out any important information that would be helpful in solving this. Thank you.

Answer 1

If you set \begin{align} y' = \frac{2x+y}{3} \ \ \text{ and } \ \ x' = x \end{align} then you will see that \begin{align} 3y'=2x'+y \ \Rightarrow \ \ y = 3y'-2x'. \end{align}