Question

Which statement best explains whether △JKL is congruent to △MNP?

△JKL is congruent to △MNP because △JKL can be mapped to △MNP by a rotation of 180° about the origin followed by a translation 2 units up.
△JKL is not congruent to △MNP because there is no sequence of rigid motions that maps △JKL to △MNP.
△JKL is congruent to △MNP because △JKL can be mapped to △MNP by a reflection across the y-axis.
​ △JKL is congruent to △MNP because △JKL can be mapped to △MNP by a reflection across the x-axis followed by a rotation of 180° about the origin.

Two triangles are graphed on a coordinate plane. The horizontal x-axis ranges from negative 5 to 5 in increments of 1. The vertical y-axis ranges from negative 5 to 5 in increments of 1. In triangle J K L, the vertex labeled as J lies on begin ordered pair negative 4 comma 2 end ordered pair. The vertex labeled as K lies on begin ordered pair negative 2 comma 3 end ordered pair. The vertex labeled as L lies on begin ordered pair negative 2 comma negative 1 end ordered pair. In triangle M N P, the vertex labeled as M lies on begin ordered pair 4 comma 0 end ordered pair. The vertex labeled as N lies on begin ordered pair 2 comma negative 1 end ordered pair. The vertex labeled as P lies on begin ordered pair 2 comma 3 end ordered pair.

Answer 1

Rotation of triangle JKL by 180 degrees will result in a triangle with corresponding vertices of (2, 4), (3, 2) and (-1, 2).

Then translating the resulting triangle 2 units up will result in a triangle with corresponding vertices (4, -2), (2, -3) and (2, 1) which is the same triangle as the given triangle MNP.

Therefore, the statement that best explains whether △JKL is congruent to △MNP is △JKL is congruent to △MNP because △JKL can be mapped to △MNP by a rotation of 180° about the origin followed by a translation 2 units up.

Answer 2

Answer:

Answer is △JKL is congruent to △MNP because △JKL can be mapped to △MNP by a rotation of 180° about the origin followed by a translation 2 units up.

Step-by-step explanation:   Because reflection is like a mirror and rotation is rotated and just by carefully looking at the shape the answer is rotation.