What are the values of x and y such that abcd=pqrs?

  T(x, y) = T(0, -8)

Step-by-step explanation:

The first reflection can be represented as ...

  (x, y) ⇒ (-x, y)

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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)

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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)

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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.