which sequence of transformations is required to create the image of rooftop 2 from the pre-image of rooftop 1-please explain!!

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  F or J

Step-by-step explanation:

The final two transformations in all choices are ...

If the rotation is clockwise, the translated figure must have a shape like this:

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Such a shape can be obtained only by reflection across the east-west street. As the first attachment shows, translation east of the reflected figure, then rotation 90° CW will locate Rooftop 2 approximately as shown in the given drawing.

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If the rotation is counterclockwise, the translated figure must have a shape like this:

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This shape can only be obtained by reflection across the north-south street. That reflection and subsequent translation will leave the figure north of the east-west street. A 90° CCW rotation about a suitably chosen point can place it south of the east-west street, in the location shown in the given drawing.

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The first attached figure was obtained by the sequence described in choice F. The second attached figure was obtained by the sequence described in choice J. The sequence of transformations is shown as red after the reflection, purple after the translation east, then blue after the rotation about the indicated point.

Both F and J are appropriate answer choices.

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Additional comment

It can be proven algebraically that choices F and J can both produce exactly the same transformation for some combination of translation and center of rotation. It seems likely that one of these answers will be preferred by your computer. You may want to discuss this question with your teacher.

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step-by-step explanation: