Question

△QRS is mapped to △Q'R'S' using the rules (x, y)→(−x, y) followed by (x, y)→(x−1, y+2).



Which statement describes the relationship between △QRS and △Q'R'S'?

Responses

△QRS is congruent to △Q'R'S' because the rules represent a translation followed by a rotation, which is a sequence of rigid motions.
triangle Q R S is congruent to triangle Q prime R prime S prime because the rules represent a translation followed by a rotation, which is a sequence of rigid motions.

△QRS is not congruent to △Q'R'S' because the rules do not represent a sequence of rigid motions.
triangle Q R S is not congruent to triangle Q prime R prime S prime because the rules do not represent a sequence of rigid motions.

△QRS is congruent to △Q'R'S' because the rules represent a reflection followed by a translation, which is a sequence of rigid motions.
triangle Q R S is congruent to triangle Q prime R prime S prime because the rules represent a reflection followed by a translation, which is a sequence of rigid motions.

△QRS is congruent to △Q'R'S' because the rules represent a reflection followed by a rotation, which is a sequence of rigid motions.

Answer 1

△QRS is congruent to △Q'R'S' because the rules represent a reflection ((x,y)→(−x,y)) followed by a translation ((x,y)→(x−1,y+2)), and a reflection plus a translation are rigid motions that preserve shape and size.