Final answer:
The correct set of transformations to prove that Δqrs and Δuts are congruent would be option 2, which involves reflecting Δuts over the line y = 2 and then translating the result by the rule (x + 2, y + 0).
Step-by-step explanation:
The question asks about a set of transformations that would prove two triangles, Δqrs and Δuts, are congruent. To find which set of transformations can prove the congruence, one must carefully consider the transformations provided to see which could make the triangles coincide exactly without altering their shape or size - only their position and orientation.
Reflecting over a line and then translating or dilating can prove congruence if the transformations appropriately place one triangle onto the other with corresponding sides and angles matching. However, dilation changes size and thus would not prove congruence unless the dilation factor is 1. So we can dismiss option 1 right away. Reflection followed by a translation is a plausible sequence of transformations that could demonstrate congruence if it correctly repositions the triangle without altering its dimensions.
Looking over the given choices, only option 2 provides a sequence that maintains the size and shape of the triangle while possibly reorienting it to match the other triangle exactly (Δqrs), assuming the reflection places the two triangles in corresponding positions.