Question

Let P be the transformation representing a reflection over the line y=b and let Q be the transformation representing a reflection over the line y=a, where a < b. Describe a single transformation that would give the same results as P∘Q, if the preimage isn't on neither line y = a nor the line y = b.

Answer 1

P: (x,y) → (x,b-(y-b)) = (x,2b-y)
Q: (x,y) → (x,2a-y)
P∘Q: (x,y) → (x,2a-(2b-y)) = (x,2a-2b+y)

Answer 2

Since b > a, it should be (x, 2b-2a+y)