Question

he coordinates of the vertices of △JKL are J(3, 0) , K(1, −2) , and L(6, −2) . The coordinates of the vertices of △J′K′L′ are J′(−3, 1) , K′(−1, 3) , and L′(−6, 3) .



Which statement correctly describes the relationship between △JKL and △J′K′L′ ?


△JKL is congruent to △J′K′L′ because you can map △JKL to △J′K′L′ using a translation 1 unit up followed by a reflection across the y-axis, which is a sequence of rigid motions.

△JKL is congruent to △J′K′L′ because you can map △JKL to △J′K′L′ using a rotation of 180° about the origin followed by a translation 1 unit up, which is a sequence of rigid motions.

△JKL is congruent to △J′K′L′ because you can map △JKL to △J′K′L′ using a reflection across the x-axis followed by a reflection across the y-axis, which is a sequence of rigid motions.

△JKL is not congruent to △J′K′L′ because there is no sequence of rigid motions that maps △JKL to △J′K′L′.

Answer 1

Rotation of 180° about the origin gives:

( x, y ) → ( - x, - y )   ( image )

J ( 3, 0 ) → ( - 3, 0 );    K ( 1, - 2 ) → ( - 1 , 2 ) ;     L ( 6, - 2 ) → ( - 6, 2 )

After that - translation 1 unit up gives:

J` ( -3, 0 + 1 ) = ( - 3 , 1 ) ; K` ( - 1 , 2 + 1 ) = ( - 1. 3 ); L`( - 6 , 2 + 1 ) = (  - 6 , 3 )

It proves that the correct option is B.

Answer: B. Triangles are congruent because you can map ΔJKL to ΔJ`K`L` using a rotation of 180° about the origin followed by a translation 1 unit up, which is a sequence of rigid motions.