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.

Question

Mathematics

Jamar Frank

9 July, 06:29

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.

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Doll · Answer 1

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.