Question

The coordinates of the vertices of △JKL are J(−2, 1) , K(−1, 3) , and L(−3, 4) . The coordinates of the vertices of △J′K′L′ are J′(−2, −1) , K′(−1, −3) , and L′(−3, −3) .

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


A) △JKL is congruent to △J′K′L′ because you can map △JKL to △J′K′L′ using a reflection across the y-axis, which is a rigid motion.

B) △JKL is congruent to △J′K′L′ because you can map △JKL to △J′K′L′ using a translation 2 units down, which is a rigid motion.

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

D) △JKL is congruent to △J′K′L′ because you can map △JKL to △J′K′L′ using a reflection across the x-axis, which is a rigid motion.

Answer 1

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

Answer 2

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

Explanation:

If L' were (-3,-4), it would be a reflection of L across the x-axis as J' and K' are with respect to J and K. Unfortunately, because it is not, the side lengths J'L' and K'L' of triangle J'K'L' are different from those of triangle JKL. This ensures the triangles JKL and J'K'L' are not congruent.