Question

Quadrilaterals EFGH and ABCD are congruent. Which of the following sequences of transformations maps EFGH onto ABCD?

Sequence A:
A -90⁰ rotation about point H, then a translation along the directed line segment HD

Sequence B:
A -90⁰ rotation about point F, then a translation along the directed line segment FA

A) Only sequence A
B) Only sequence B
C) Both
D) Neither​

Answer 1

(A) Only sequence A

Explanation:

You want the sequence of transformations that maps parallelogram EFGH to ABCD.

Rotation

We note that segment EF points to the right, and corresponding segment AB points down. The rotation required to change the direction in that way is a rotation of -90°, that is, 90° CW.

Translation

The translation that will work in this context is translation of the center of rotation to its corresponding point on the image. The given choices of center are ...

• point H
• point F

Point H corresponds to point D, so the translation vector would need to be HD after rotation about point H. This matches sequence A.

Point F corresponds to point B, so the translation vector would need to be FB after rotation about point F. Sequence B erroneously has the vector as FA.

Only sequence A maps EFGH to ABCD, choice A.

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