Pedro was curious if circles $${A}$$ and $${B}$$ (with $${X}$$ and $${Y}$$ being on each circle, respectively) were similar, so he tried to map one figure onto the other using rigid transformations. ![](http://admin.getprephub.com/media/editor/si1_20230201184415906911.png) Pedro concluded: "It's not possible to map circle A onto circle B using a sequence of rigid transformations, so the circles are not similar." \section{What error did Pedro make in his conclusion?}

If a sequence of rigid transformations (translations, reflections, and rotations) and dilations can map circle A onto circle B, then the figures are similar. Here Pedro performed a translation so point A coincides with point B. ![](http://admin.getprephub.com/media/editor/si1s_20230201184437230264.png) If we dilate by a factor of $$\frac{1}{2}$$ about point $$B$$. ![](http://admin.getprephub.com/media/editor/si1ss_20230201184454980395.png) The pre-image, circle $$A$$, maps exactly onto circle $$B$$. Pedro concluded: "It's not possible to map circle A onto circle B using a sequence of rigid transformations, so the circles are not similar." One more transformation - a dilation - would map circle A onto circle B. So the circles are similar.

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Pedro was curious if circles ${A}$ and ${B}$ (with ${X}$ and ${Y}$ being on each circle, respectively) were similar, so he tried to map one figure onto the other using rigid transformations.

Pedro concluded:

“It’s not possible to map circle A onto circle B using a sequence of rigid transformations, so the circles are not similar.”

\section{What error did Pedro make in his conclusion?}

Select all that apply :

One more transformation - a dilation - would map circle A onto circle B. So the circles are similar.

One more transformation - a rotation - would map circle A onto circle B. So the circles are similar.

None of the above

There is no error. This is a correct conclusion

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