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 reflection across the x-axis 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 not congruent to △J′K′L′ because there is no sequence of rigid motions that maps △JKL to △J′K′L′.

Answer 1

Check the picture:

Rotating JKL 180° with respect to the origin, and translating it 1 unit up, we get J'K'L'.

That is, the 2 triangles match perfectly.


Answer: 
△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.

Answer 2

Answer:

As Given :The 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) .

⇒As we can see the two triangles are congruent because length of sides are equal.i.e By SSS  ΔJKL and ΔJ'K'L' are congruent.

⇒ As you can see from the figure depicted below the triangle JKL is rotated by an angle of 180° then translation of y coordinate by 1 unit up has taken place.

So , Option (3) is correct which is :△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.