Question

Triangles Q R S and T U V are shown. Triangle Q R S is translated across S Q and then is shifted down and to the right to form triangle T U V.
Can a translation and a reflection map TriangleQRS to TriangleTUV? Explain why or why not.

No, the triangles are not congruent.
Yes, a translation mapping vertex Q to vertex T and a reflection across the line containing QS will map
△QRS to △TUV.
No, the triangles are obtuse.
Yes, a translation mapping vertex S to vertex T and a reflection across the line containing RS will map
△QRS to △TUV.

Answer 1

Yes — the second choice is correct:

A translation that sends Q to T followed by a reflection across the line containing QS will carry △QRS onto △TUV. Translations and reflections are rigid motions, so they preserve distances and angles (the triangles are congruent), and the reflection across the line through Q and S sends the third vertex to its mirror image on the other side of that line, yielding the vertices T, U, V in the correct positions.