Question

quadrilaterals efgh and abcd are congruent.
which of the following sequences of transformations maps efgh onto abcd?
sequence a
a -90° rotation about point h, then a translation along the directed line segment hd.
sequence b
a -90° rotation about point f, then a translation along the directed line segment fa.
choose 1 answer:
only sequence a
only sequence b
both
neither

Explanation:

Step1: Analyze Sequence A

A \(-90^\circ\) (clockwise) rotation about point \(H\) will rotate \(EFGH\). Then, translating along \(\overrightarrow{HD}\) (from \(H\) to \(D\)) should map \(EFGH\) to \(ABCD\) as the congruent quadrilaterals' positions suggest this transformation works.

Step2: Analyze Sequence B

A \(-90^\circ\) rotation about point \(F\), followed by translation along \(\overrightarrow{FA}\) (from \(F\) to \(A\)): The rotation about \(F\) and subsequent translation would not align \(EFGH\) to \(ABCD\) as the center of rotation and translation vector don't match the required transformation to reach \(ABCD\) from \(EFGH\). So only Sequence A works.

Answer:

Only sequence A (the option with "Only sequence A" text, likely the first option among the choices presented as a radio button with that label)