Question

△ qrs is mapped to △ qrs using the rules (x, y) → (-x, y) followed by (x, y) → (x - 1, y + 2) which statement describes the relationship between △ qrs and △ qrs? ○ △ qrs is congruent to △ qrs because the rules represent a reflection followed by a translation, which is a sequence of rigid motions. ○ △ qrs is not congruent to △ qrs because the rules do not represent a sequence of rigid motions. ○ △ qrs is congruent to △ qrs because the rules represent a reflection followed by a rotation, which is a sequence of rigid motions. ○ △ qrs is congruent to △ qrs because the rules represent a translation followed by a rotation, which is a sequence of rigid motions.

Explanation:

Rigid motions (reflection, translation, rotation) preserve congruence. The first rule $(x,y)\to(-x,y)$ is a reflection (rigid), and the second $(x,y)\to(x-1,y+2)$ is a translation (rigid). Their sequence maintains congruence.

Answer:

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