Triangles $$\triangle P Q R$$ and $$\triangle A B C$$ are congruent. The side length of each square on the grid is 1 unit. ![](http://admin.getprephub.com/media/editor/pt11_20230125194347941315.png) Which of the following sequences of transformations maps $$\triangle {PQR}$$ onto $$\triangle {ABC}$$ ? ![](http://admin.getprephub.com/media/editor/pt11s_20230125194407342009.png)

Answer If we draw each of the sequences and see if they map $$\triangle P Q R$$ onto $$\triangle A B C$$. In Sequence A we perform a $$180^{\circ}$$ rotation about point $${R}$$. ![](http://admin.getprephub.com/media/editor/pt11ss_20230125194426606242.png) then a translation 2 units to the right and 6 units up. ![](http://admin.getprephub.com/media/editor/pt11sss_20230125194441529321.png) We can see that this sequence does not map $$\triangle P Q R$$ onto $$\triangle A B C$$. In Sequence B we perform a translation 4 units to the right and 6 units up. ![](http://admin.getprephub.com/media/editor/pt11ssss_20230125194502578930.png) then a reflection over the horizontal line through point $$A$$. ![](http://admin.getprephub.com/media/editor/pt11sssss_20230125194523245374.png) We can see that this sequence does not map $$\triangle P Q R$$ onto $$\triangle A B C$$. In conclusion, neither of the sequences maps $$\triangle P Q R$$ onto $$\triangle A B C$$.

Prephub

Triangles $\triangle P Q R$ and $\triangle A B C$ are congruent. The side length of each square on the grid is 1 unit.

Which of the following sequences of transformations maps $\triangle {PQR}$ onto $\triangle {ABC}$ ?

Neither

Only sequence $A$

Only sequence $B$

Both

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