Question

Triangles QRS and TUV are shown. Triangle QRS is translated across SQ and then shifted down and to the right to form triangle TUV. Can a translation and a reflection map Triangle QRS to Triangle TUV? Explain why or why not.

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

Answer 1

A translation mapping vertex Q to vertex T and a reflection across the line containing QS can map Triangle QRS to Triangle TUV if they are congruent, with option B being correct.

Step-by-step explanation:

The student asks if a translation and a reflection can map Triangle QRS to Triangle TUV. Assuming triangles QRS and TUV are congruent and that the translation does not alter the size or shape of the triangles, only their positions, this mapping is indeed possible. The correct option would be B, which states Yes, a translation mapping vertex Q to vertex T and a reflection across the line containing QS will map △QRS to △TUV.

A translation involves sliding the figure in any direction without changing its size, orientation, or shape. A reflection flips the figure over a line, creating a mirror image. Therefore, a reflection over line QS followed by a translation can reposition Triangle QRS to coincide with Triangle TUV, preserving congruency and orientation.