Question

The rule (x,y)→(2x,2y) maps △DEF to △D′E′F′.

Which statement correctly describes the relationship between △DEF and △D′E′F′ ?
the triangles are congruent because △D′E′F′ is a rotation of △DEF , and a rotation is a rigid motion.

The triangles are congruent because △D′E′F′ is a reflection of △DEF , and a reflection is a rigid motion.

The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.

The triangles are not congruent because △D′E′F′ is a translation of △DEF , and a translation is not a rigid motion.

Answer 1

The rule: (x,y)→(2x,2y), mapping △DEF to △D′E′F′ can be described as a dilation of △DEF into △D′E′F′. The points are extended away from each other by increasing their distance from the origin, making △D′E′F′ larger than △DEF. A dilation is not a rigid motion, because distance between the points D, E, and F are not preserved, but extended. The triangles are not congruent because they change size.

Answer 2

The rule (x,y)→(2x,2y) maping △DEF to △D′E′F′ is a dilation which enlarges the pre-image by a scale of 2.

Two triangle are congruent when all the corresponding angles are equal and all the corresponding sides are equal.

Therefore, the triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.