Question

What transformation moves R (r (P)) back to P, given that R(x, y) = (-2, -y) and r (x, y) = (x, -y)?

Answer 1

First, find where would the point P(x,y) would land after applying the transformatios r and R:

`R(r(P))=R(r(x,y))=R(x,-y)=(-x,y)`

Notice that it would be enough to flip the sign of the first coordinate to send (-x,y) back to (x,y).

Then, the transformation that moves R(r(P)) back to P is:

`(x,y)\rightarrow(-x,y)`

Therefore, the answer is:

`(-x,y)`