Question

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

I can’t decide which choice is correct without seeing the picture (or being given coordinates or side lengths). Give me the diagram or the coordinates of Q,R,S and T,U,V and I’ll pick and justify the correct choice.

How to tell yourself:
- First check congruence: compute the three side lengths of △QRS and △TUV. If they are not all equal pairwise, any rigid motion (translation + reflection included) cannot map one to the other, so the correct answer is “No, the triangles are not congruent.”
- If the side lengths match, the triangles are congruent. A single reflection changes orientation, a translation does not, so the composition “translation then reflection” is an isometry that can place one congruent triangle on the other if the triangles are mirror images in the correct way.
- To find the specific mapping: pick a corresponding vertex (for example Q→T or S→T). Translate △QRS so that that vertex lands on the chosen corresponding vertex. Then see whether reflecting across the line containing the appropriate side of the translated triangle (for instance the line through the two vertices that should correspond to the given side) carries the other two vertices to the remaining vertices T,U,V. If it does, that “Yes” answer with that vertex/line is correct; if it does not, try the other correspondence.

If you paste the diagram or coordinates I’ll check the lengths and show the required translation and reflection (and then pick the correct multiple‑choice answer).