Question

parallelogram defg has been rotated. which statements are correct? check all that apply. point f → point f parallelogram defg → parallelogram gfed point d of the pre - image corresponds to point d of the image. (overline{ed}) of the pre - image corresponds to (overline{gf}) of the image. parallelogram defg maps to parallelogram defg.

Explanation:

Step1: Recall rotation property

In a rotation, each point of the pre - image has a corresponding point in the image.

Step2: Analyze point - to - point correspondence

For a rotated figure, point \(F\) in the pre - image corresponds to point \(F'\) in the image. So, "point \(F
ightarrow\) point \(F'\)" is correct.

Step3: Analyze figure - to - figure correspondence

The pre - image parallelogram \(DEFG\) maps to the image parallelogram \(D'E'F'G'\), not \(G'F'E'D'\). So, "parallelogram \(DEFG
ightarrow\) parallelogram \(G'F'E'D'\)" is incorrect.

Step4: Analyze point correspondence

Point \(D\) of the pre - image corresponds to point \(D'\) of the image. This is correct as per the rotation mapping.

Step5: Analyze side correspondence

In a rotation, \(\overline{ED}\) of the pre - image corresponds to \(\overline{E'D'}\), not \(\overline{G'F'}\). So, "\(\overline{ED}\) of the pre - image corresponds to \(\overline{G'F'}\) of the image" is incorrect.

Step6: Analyze figure mapping

Parallelogram \(DEFG\) maps to parallelogram \(D'E'F'G'\) which is correct.

Answer:

point \(F
ightarrow\) point \(F'\)
Point \(D\) of the pre - image corresponds to point \(D'\) of the image.
Parallelogram \(DEFG\) maps to parallelogram \(D'E'F'G'\)