Question

△DEF is mapped to △D′E′F′ using the rule (x,y)→(x,y+1) followed by (x,y)→(x,−y).

Which statement correctly describes the relationship between △DEF and △D′E′F′ ?

△DEF is not congruent to △D′E′F′ because the rules do not represent a sequence of rigid motions.

△DEF is congruent to △D′E′F′ because the rules represent a translation followed by a rotation, which is a sequence of rigid motions.

△DEF is congruent to △D′E′F′ because the rules represent a translation followed by a reflection, which is a sequence of rigid motions.

△DEF is congruent to △D′E′F′ because the rules represent a reflection followed by a reflection, which is a sequence of rigid motions.

Answer 1

ΔDEF is congruent to ΔD'E'F' because the rules represent a translation followed by a reflection, which is a sequence of rigid motions.

Answer 2

Answer:△DEF is congruent to △D′E′F′ because the rules represent a translation followed by a reflection, which is a sequence of rigid motions.

Explanation:

A rigid motion of the plane is a motion which maintain distance.

Translation is a kind of rigid motion used in geometry to trace a function that moves an object a particular distance.

A reflection is also a kind of rigid motion . It is mainly a 'toss' of a shape across the line of reflection.

So,△DEF is mapped to △D′E′F′ using the rule (x,y)→(x,y+1) ( which is a translation.) followed by (x,y)→(x,−y)(which is reflection),therefore it is a sequence of rigid motions.