Triangle xyz is translated by the rule (x + 1, y − 1) and then dilated by a scale factor of 4 centered at the origin. which statement describes the properties of triangles xyz and x''y''z'' after the transformations?

y and ∠y'' are congruent after the translation, but not after the dilation.

∠y and ∠y'' are congruent after the dilation, but not after the translation.

segment yz and segment y double prime z double prime are proportional after the translation, but not after the dilation.

segment yz and segment y double prime z double prime are proportional after the dilation and congruent after the translation.

Option D.

Step-by-step explanation:

Translation: It is a rigid transformation. It means size and shape of the figure remains same after translation. In translation, a figure is shifted from one place to another without any other changes.

It means corresponding angles and sides are congruent after the translation.

Dilation: It is the enlargement or reduction of a figure. In dilation, the shape of image and preimage are same but the size is different.

It means corresponding angles are congruent after but sides are proportional after the dilation.

        (After the translation and dilation)

So, options A and B are incorrect.

YZ and Y''Z'' are proportional after the dilation and congruent after the translation.

Therefore, the correct option is D.