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△ABC is mapped to △A′B′C′ using the rule (x, y)→(−x, −y) followed by (x, y)→(x, −y) .



Which statement correctly describes the relationship between △ABC and △A′B′C′ ?


A. △ABC is congruent to △A′B′C′ because the rules represent a reflection followed by a rotation, which is a sequence of rigid motions.

B. △ABC is congruent to △A′B′C′ because the rules represent a rotation followed by a reflection, which is a sequence of rigid motions.

C. △ABC is not congruent to △A′B′C′ because the rules do not represent a sequence of rigid motions.

D. △ABC is congruent to △A′B′C′ because the rules represent a reflection followed by a reflection, which is a sequence of rigid motions.

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Answer:

B. △ABC is congruent to △A′B′C′ because the rules represent a rotation followed by a reflection, which is a sequence of rigid motions.

Step-by-step explanation:

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Transformation involves changing the position of a shape.

The correct statement is: (b) △ABC is congruent to △A′B′C′ because the rules represent a rotation followed by a reflection, which is a sequence of rigid motions.

The transformation rule is given as:

[tex]\mathbf{(x,y) \to (-x,-y)}[/tex], then:

[tex]\mathbf{(x,y) \to (x,-y)}[/tex]

  • The first transformation [tex]\mathbf{(x,y) \to (-x,-y)}[/tex] is 180 degrees rotation across the origin
  • The second transformation [tex]\mathbf{(x,y) \to (x,-y)}[/tex] is a reflection across the x-axis

Rotation and reflection are both rigid transformation.

Hence, the correct option is (b):

Read more about rotation and reflection at:

https://brainly.com/question/15577335

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