Quadrilaterals EFGH and $${ABCD}$$ are congruent.

![](http://admin.getprephub.com/media/editor/pt12_20230125194551935044.png)

Which of the following sequences of transformations maps EFGH onto ABCD?

![](http://admin.getprephub.com/media/editor/pt12s_20230125194610130587.png)

<div id="displayOption0" class="markdown-body editormd-html-preview"><textarea>Only sequence $$A$$

</textarea>Only sequence <math><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math>A
</div>

<div id="displayOption1" class="markdown-body editormd-html-preview"><textarea>Only sequence $$B$$

</textarea>Only sequence <math><semantics><mrow><mi>B</mi></mrow><annotation encoding="application/x-tex">B</annotation></semantics></math>B
</div>

<div id="displayOption3" class="markdown-body editormd-html-preview"><textarea>Neither

</textarea>Neither
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<div id="id_cont_display" class="markdown-body editormd-html-preview"><textarea>Quadrilaterals EFGH and $${ABCD}$$ are congruent.

![](http://admin.getprephub.com/media/editor/pt12_20230125194551935044.png)

Which of the following sequences of transformations maps EFGH onto ABCD?

![](http://admin.getprephub.com/media/editor/pt12s_20230125194610130587.png)</textarea>Quadrilaterals EFGH and <math><semantics><mrow><mrow><mi>A</mi><mi>B</mi><mi>C</mi><mi>D</mi></mrow></mrow><annotation encoding="application/x-tex">{ABCD}</annotation></semantics></math>ABCD are congruent.
<img src="http://admin.getprephub.com/media/editor/pt12_20230125194551935044.png" alt="">
Which of the following sequences of transformations maps EFGH onto ABCD?
<img src="http://admin.getprephub.com/media/editor/pt12s_20230125194610130587.png" alt="">
</div>

<div id="id_solution_display" class="markdown-body editormd-html-preview"><textarea>Answer

In Sequence $$A$$ we perform a $$-90^{\circ}$$ rotation about point $${H}$$ (clockwise)... 

![](http://admin.getprephub.com/media/editor/pt12ss_20230125194624134163.png)

then a translation along the directed line segment $$\overline{H D}$$.

![](http://admin.getprephub.com/media/editor/pt12sss_20230125194714390510.png)
We can see that this sequence does map EFGH onto ABCD.

In Sequence $$B$$ we perform $$a-90^{\circ}$$ rotation about point $$F$$ 

![](http://admin.getprephub.com/media/editor/pt12ssss_20230125194641307925.png)


then a translation along the directed line segment FA.

![](http://admin.getprephub.com/media/editor/pt12sssss_20230125194736283067.png)

We can see that this sequence does not map EFGH onto ABCD.

In conclusion, only sequence A maps EFGH onto ABCD.

</textarea>Answer
In Sequence <math><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math>A we perform a <math><semantics><mrow><mo>−</mo><mn>9</mn><msup><mn>0</mn><mrow><mo>∘</mo></mrow></msup></mrow><annotation encoding="application/x-tex">-90^{\circ}</annotation></semantics></math>−90​∘​​ rotation about point <math><semantics><mrow><mrow><mi>H</mi></mrow></mrow><annotation encoding="application/x-tex">{H}</annotation></semantics></math>H (clockwise)… 
<img src="http://admin.getprephub.com/media/editor/pt12ss_20230125194624134163.png" alt="">
then a translation along the directed line segment <math><semantics><mrow><mover accent="true"><mrow><mi>H</mi><mi>D</mi></mrow><mo stretchy="true">‾</mo></mover></mrow><annotation encoding="application/x-tex">\overline{H D}</annotation></semantics></math>​HD​​​.
<img src="http://admin.getprephub.com/media/editor/pt12sss_20230125194714390510.png" alt=""> We can see that this sequence does map EFGH onto ABCD.
In Sequence <math><semantics><mrow><mi>B</mi></mrow><annotation encoding="application/x-tex">B</annotation></semantics></math>B we perform <math><semantics><mrow><mi>a</mi><mo>−</mo><mn>9</mn><msup><mn>0</mn><mrow><mo>∘</mo></mrow></msup></mrow><annotation encoding="application/x-tex">a-90^{\circ}</annotation></semantics></math>a−90​∘​​ rotation about point <math><semantics><mrow><mi>F</mi></mrow><annotation encoding="application/x-tex">F</annotation></semantics></math>F 
<img src="http://admin.getprephub.com/media/editor/pt12ssss_20230125194641307925.png" alt="">
then a translation along the directed line segment FA.
<img src="http://admin.getprephub.com/media/editor/pt12sssss_20230125194736283067.png" alt="">
We can see that this sequence does not map EFGH onto ABCD.
In conclusion, only sequence A maps EFGH onto ABCD.
</div>