Question

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?

Answer 1

Using the given transformations, namely translation and dilation, the correct statement is given as follows:

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

Translation

The translation rule in this problem is given as follows:

(x, y) -> (x + 1, y - 1).

Meaning that the triangle was shifted:

• One unit right, due to x -> x + 1.

• One unit down, due to y -> y - 1.

The only change with the dilation was in the position of the triangle, hence the translated triangle is congruent to the original triangle.

Dilation

The triangle was dilated by a scale factor of 4, meaning that the coordinates of each vertex of the triangle is multiplied by 4, changing the side lengths of the triangle, thus the dilated triangle is not congruent to the original triangle.

The angles keep the same measure for both cases, translation and dilation, hence the first two statements are incorrect.

The change in the side lengths is proportional, due to the scale factor of 4, hence the correct statement is:

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

What is the missing information?

The correct options are missing and are given by the image at the end of the answer.

More can be learned about transformations at brainly.com/question/28174785

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