Question

select the correct answer. shape 1 and shape 2 are plotted on a coordinate plane. which statement about the shapes is true? a. shape 1 is congruent to shape 2, which can be shown using a sequence of dilations and translations. b. shape 1 is not congruent to shape 2 because the shapes do not have the same absolute coordinates. c. shape 1 is congruent to shape 2, which can be shown using a translation. d. shape 1 is not congruent to shape 2 because a sequence of rigid transformations will not map shape 1 onto shape 2

Explanation:

Step1: Recall congruence definition

Two shapes are congruent if one can be mapped onto the other using rigid - transformations (translations, rotations, reflections). Dilations change the size of a shape and non - rigid transformations are not allowed for congruence.

Step2: Analyze option A

Dilations change the size of a shape. Congruent shapes must have the same size and shape. So, a sequence of dilations and translations cannot be used to show congruence between two congruent shapes. Option A is incorrect.

Step3: Analyze option B

The absolute coordinates of a shape do not determine congruence. Congruence is about the size and shape of the figure, not its position on the coordinate plane. Option B is incorrect.

Step4: Analyze option C

Just a translation alone will not map shape 1 onto shape 2 as they are not in the same orientation and position that can be achieved by just a translation. Option C is incorrect.

Step5: Analyze option D

Since a sequence of rigid transformations (translations, rotations, reflections) will not map shape 1 onto shape 2, shape 1 is not congruent to shape 2. Option D is correct.

Answer:

D. Shape 1 is not congruent to shape 2 because a sequence of rigid transformations will not map shape 1 onto shape 2.