Answer:
T(x, y) = T(0, -8)
Explanation:
The first reflection can be represented as ...
(x, y) ⇒ (-x, y)
__
The rotation about the origin is the transformation ...
(x, y) ⇒ (-x, -y)
so the net effect of the first two transforms is ...
(x, y) ⇒ (x, -y)
__
Then the reflection across y=4 alters the y-coordinate:
(x, y) ⇒ (x, 8-y)
so the net effect of the three transforms is ...
(x, y) ⇒ (x, 8+y)
__
In order to bring the figure back to place, we must translate it down 8 units using ...
(x, y) ⇒ (x, y-8) . . . . net effect: (x, y) ⇒ (x, (8+y)-8) = (x, y)
The translation is by 0 units in the x-direction and -8 units in the y-direction.