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 and transformations

Congruent shapes have same size and shape. Rigid transformations (translation, rotation, reflection) preserve congruence; dilation (scaling) does not. So if dilation is used, shapes aren't congruent.

Step2: Analyze Option A

Option A says congruent via dilations and translations. But dilation changes size, so congruent shapes can't use dilation. Eliminate A.

Step3: Analyze Option B

Congruence doesn't depend on same coordinates (translation moves shapes). So B's reasoning is wrong. Eliminate B.

Step4: Analyze Option C

Check if translation maps shape1 to shape2. Visually, shape2 is larger (taller, wider) than shape1. Translation preserves size, so they can't be congruent via translation. Eliminate C.

Step5: Analyze Option D

Since shape2 is larger (so size differs), rigid transformations (which preserve size) can't map shape1 to shape2. So shape1 is not congruent to shape2. 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.