Aparallelogram is transformed according to the rule (x, y) → (x, y). which is another way to state the transformation?

If it is said that a parallelogram has transformed according to  (x, y) → (x, y), then no transformation has occurred. a transformation happens when there is a change in either x or y, or both. to say for example, a parallelogram that undergoes transformation given by (x, y) → (x, -y) would be experiencing an x-axis reflection. similarly, a transformation given by  ( x, y) → (-x, y) would mean a y-axis reflection.