Question

analyzing possible transformations
during geometry class, students are told that ( \triangle tsrcong\triangle usv ). marcus states that ( \triangle tsr ) is mapped to ( \triangle usv ) by performing a rotation about point s. sam states that ( \triangle tsr ) is mapped to ( \triangle usv ) by a reflection across the line that goes through point s. determine if either student is correct.
sam is correct
marcus is correct
both students are correct.
neither student is correct

Explanation:

A rotation about a point changes the orientation of a figure. A reflection across a line (in this case, the line through point \(S\)) can map \(\triangle TSR\) to \(\triangle USV\) as it creates a mirror - image. A rotation about point \(S\) would not map \(\triangle TSR\) to \(\triangle USV\) because the orientation change due to rotation (unless it's a \(180^{\circ}\) rotation, but there's no indication of that from the general property of rotation about a point for congruent triangles in this non - \(180^{\circ}\) - specific context) is not the correct transformation here. Reflection across the line through \(S\) is the valid transformation.

Answer:

Sam is correct.