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The coordinates of the vertices of △PQR are P(1, 4) , Q(2, 2) , and R(−2, 1) . The coordinates of the vertices of △P′Q′R′ are P′(−1, 4) , Q′(−2, 2) , and R′(2, 1) . △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.

Respuesta :

Answer:

The coordinates of the vertices of △ABC are A(1, 4) , B(2, 2) , and C(−2, 1) . The coordinates of the vertices of △A′B′C′ are A′(−1, 4) , B′(−2, 2) , and C′(2, 1) . △ABC is mapped to △A′B′C′ using the rule (x, y)→(−x, −y) followed by (x, y)→(x, −y).

As shown in the figure below

A(1,4)→A''(-1,-4)

B(2,2)→B''(-2,-2)

C(-2,1)→C''(2,-1)

⇒ΔABC≅ΔA''B''C''

Reflection along the line  y= x, which passes through the origin

then, Reflection along X axis has taken place.

A''(-1,-4)→ A′(−1, 4)

B''(-2,-2)→B′(−2, 2)

C''(2,-1)→C′(2, 1)

⇒ΔABC≅ΔA'B'C'

Option (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 is correct.


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