Question

The coordinates of the vertices of AJKL are J(3, 0), K(1, -2), and L(6, -2). The coordinates of the vertices of AJ'K'L' are J'(-3, 1), K'(-1, 3), and L'(-6, 3). Which statement correctly describes the relationship between AJKL and AJ'K'L'?

A) AJKL is congruent to AJ'K'L' because you can map AJKL to AJ'K'L' using a rotation of 180° about the origin followed by a translation 1 unit up, which is a sequence of rigid motions.
B) AJKL is not congruent to AJ'K'L' because there is no sequence of rigid motions that maps AJKL to AJ'K'L'.
C) AJKL is congruent to AJ'K'L' because you can map AJKL to AJ'K'L' using a reflection across the x-axis followed by a reflection across the y-axis, which is a sequence of rigid motions.
D) AJKL is congruent to AJ'K'L' because you can map AJKL to AJ'K'L' using a translation 1

Answer 1

The correct answer is B) AJKL is not congruent to AJ'K'L' because there is no sequence of rigid motions that maps AJKL to AJ'K'L'.

Step-by-step explanation:

The coordinates of the vertices indicate a translation, but the presence of negative signs in the coordinates of corresponding vertices suggests a reflection.

The transformations involved in mapping AJKL to AJ'K'L' would require both a translation and a reflection.

However, the given answer choices A, C, and D suggest single-step transformations or a combination of rotation and translation.

None of these choices accurately reflects the required sequence of transformations, which includes a translation and reflections.

Therefore, AJKL is not congruent to AJ'K'L' because there is no sequence of rigid motions presented in the answer choices that maps AJKL to AJ'K'L'.

Understanding the nature of transformations is crucial in geometry, as it allows for accurate analysis of the relationships between geometric shapes and their corresponding vertices.