Question

Triangle XYZ is translated by the rule (x + 1, y â 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 â Y'' are congruent after the translation, but not after the dilation. â Y and â Y'' are congruent after the dilation, but not after the translation. and are proportional after the translation, but not after the dilation. and are proportional after the dilation and congruent after the translation.

Answer 1

The correct option after the triangle translation is;

D) segment YZ and segment Y double prime Z double prime are proportional after the dilation and congruent after the translation.

What are the coordinates after transformation?

After translating triangle XYZ by the rule (x + 1, y − 1) and then dilating it by a scale factor of 4 centered at the origin, the statement "segment YZ and segment Y''Z'' are proportional after the dilation and congruent after the translation" describes the properties of triangles XYZ and X''Y''Z'' after the transformations.

This is because dilation by a scale factor of 4 centered at the origin results in the segments being proportional, and translation preserves the congruence of the segments.

Therefore, the correct statement is that segment YZ and segment Y''Z'' are proportional after the dilation and congruent after the translation

Complete question is;

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?

A) Y and ∠Y'' are congruent after the translation, but not after the dilation.

B) ∠Y and ∠Y'' are congruent after the dilation, but not after the translation.

C) segment YZ and segment Y double prime Z double prime are proportional after the translation, but not after the dilation.

D) segment YZ and segment Y double prime Z double prime are proportional after the dilation and congruent after the translation.

Answer 2

Answer: Y and Y'' are congruent after the translation, but not after the dilation.

Explanation:

We know that we generally prefer rigid transformations if want to create congruent images.

There are three basic kinds of rigid transformations:

1) rotation 2) reflection 3) translation

So, they all create congruent images.

But a dilation does not create congruent images because it creates an image of similar same shape as the original but not the same size.

Given : Triangle XYZ is translated and then dilated by a scale factor of 4 centered at the origin.

Then, the correct option is "Y and Y'' are congruent after the translation, but not after the dilation."