I am trying to figure out the single transformation that is equivalent to the below composition.
A glide reflection by vector $\langle−1, 1\rangle$ and reflection line $y = −x+1$, followed by translation vector $\langle−2, −2\rangle$.
$T_{\langle-2,-2\rangle}$ $∘\ G_{\langle-1,1\rangle,y=-x+1}$
This is what I have come up with. Hopefully I did this correctly. Please let me know.
$\ M_{y=-x-1}$ $∘\ M_{y=-x+1}$$∘\ M_{y=-x+1}$$∘\ T_{\langle-1,1\rangle}$ $\ M_{y=-x-1}$ $∘\ T_{\langle-1,-1\rangle}$ $\ G_{\langle-1,1\rangle,y=-x-1}$