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′? responses △def is congruent to △d′e′f′ because the rules represent a translation followed by a rotation, which is a sequence of rigid motions. triangle d e f, is congruent to , triangle d prime e prime f prime, 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. triangle d e f, is congruent to , triangle d prime e prime f prime, 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. triangle d e f, is congruent to , triangle d prime e prime f prime, because the rules represent a reflection followed by a reflection, which is a sequence of rigid motions. △def is not congruent to △d′e′f′ because the rules do not represent a sequence of rigid motions.

Answer 1

△def is congruent to △d'e'f' because both a translation and a reflection are rigid motions that preserve size and shape.

Step-by-step explanation:

The question you're asking deals with the transformations of a triangle in the coordinate plane and whether these transformations preserve congruence. When the rule (x, y) → (x, y + 1) is applied, it represents a translation one unit up along the y-axis. The next rule applied, (x, y) → (x, -y), reflects the triangle across the x-axis.

Since both a translation and a reflection are rigid motions (movements that preserve distance and angles), the size and shape of the triangle are not changed. Therefore, △def is congruent to △d'e'f' because the rules represent a sequence of rigid motions.