Which rule represents the translation from the pre-image,
DABCD, to the image. A'B'C'D'?

Step-by-step explanation:

The rest of the question is the attached figure.

As shown in the graph

The coordinates of the image ABC are:

A(-3,4) , B(-4,1) and C(-2,1)

And the coordinates of A'B'C' are:

A'(4,-2) , B'(3,-5) and C'(5,-5)

So,

A' - A = (4,-2) - (-3,4) = (7,-6) →(1)

B' - B = (3,-5) - (-4,1) = (7,-6) →(2)

C' - C = (5,-5) - (-2,1) = (7,-6) →(3)

So, from (1), (2) and (3)

The rule represents the translation form the pre image ABC to the image A’B’C’ is ⇒⇒⇒ (x, y) → (x + 7, y – 6)

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x = 3 ± √(5+y)