Circle $$A^{\prime}$$ is the result of translating circle $$A$$ by 2 units to the right and 5 units down. 

![](http://admin.getprephub.com/media/editor/tp5_20230125193300883910.png)
Select the correct statement about the unchanged properties of circle $${A}$$ and circle $${A}^{\prime}$$. 

<div id="displayOption0" class="markdown-body editormd-html-preview"><textarea>Circle $$A$$ and circle $$A^{\prime}$$ have the same area.

</textarea>Circle <math><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math>A and circle <math><semantics><mrow><msup><mi>A</mi><mrow><mi mathvariant="normal">′</mi></mrow></msup></mrow><annotation encoding="application/x-tex">A^{\prime}</annotation></semantics></math>A​′​​ have the same area.
</div>

<div id="displayOption1" class="markdown-body editormd-html-preview"><textarea>Points $$A$$ and $$A^{\prime}$$ have the same coordinates.

</textarea>Points <math><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math>A and <math><semantics><mrow><msup><mi>A</mi><mrow><mi mathvariant="normal">′</mi></mrow></msup></mrow><annotation encoding="application/x-tex">A^{\prime}</annotation></semantics></math>A​′​​ have the same coordinates.
</div>

<div id="displayOption2" class="markdown-body editormd-html-preview"><textarea>The radii of circle $$A$$ and circle $$A^{\prime}$$ have the different lengths.

</textarea>The radii of circle <math><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math>A and circle <math><semantics><mrow><msup><mi>A</mi><mrow><mi mathvariant="normal">′</mi></mrow></msup></mrow><annotation encoding="application/x-tex">A^{\prime}</annotation></semantics></math>A​′​​ have the different lengths.
</div>

<div id="displayOption3" class="markdown-body editormd-html-preview"><textarea>None of the above

</textarea>None of the above
</div>

<div id="id_cont_display" class="markdown-body editormd-html-preview"><textarea>Circle $$A^{\prime}$$ is the result of translating circle $$A$$ by 2 units to the right and 5 units down. 

![](http://admin.getprephub.com/media/editor/tp5_20230125193300883910.png)
Select the correct statement about the unchanged properties of circle $${A}$$ and circle $${A}^{\prime}$$. </textarea>Circle <math><semantics><mrow><msup><mi>A</mi><mrow><mi mathvariant="normal">′</mi></mrow></msup></mrow><annotation encoding="application/x-tex">A^{\prime}</annotation></semantics></math>A​′​​ is the result of translating circle <math><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math>A by 2 units to the right and 5 units down. 
<img src="http://admin.getprephub.com/media/editor/tp5_20230125193300883910.png" alt=""> Select the correct statement about the unchanged properties of circle <math><semantics><mrow><mrow><mi>A</mi></mrow></mrow><annotation encoding="application/x-tex">{A}</annotation></semantics></math>A and circle <math><semantics><mrow><msup><mrow><mi>A</mi></mrow><mrow><mi mathvariant="normal">′</mi></mrow></msup></mrow><annotation encoding="application/x-tex">{A}^{\prime}</annotation></semantics></math>A​′​​. 
</div>

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

Translations preserve (keep the same) angle measures and segment lengths.

Translations change the coordinates of every point in the figure.

Since a radius is a kind of segment, its length remains the same under the transformation.

Because the radius remains the same, so does the area. 

![](http://admin.getprephub.com/media/editor/tp5s_20230125193401949323.png)</textarea>Answer
Translations preserve (keep the same) angle measures and segment lengths.
Translations change the coordinates of every point in the figure.
Since a radius is a kind of segment, its length remains the same under the transformation.
Because the radius remains the same, so does the area. 
<img src="http://admin.getprephub.com/media/editor/tp5s_20230125193401949323.png" alt="">
</div>