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.

After a dilation, a figure remains proportional because its angles and betweenness of points remain the same. After a translation, the image stays congruent to the pre-image.

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andromache andromache · Answer 2 · 2021-10-28T12:47:42+02:00

The statement that described the triangle properties is that the segment YZ and segment Y"Z" should be proportional when the dilation is done and it should be congruent when the translation should be done.

Given that,

There is the rule i.e. (x +1, y - 1) and it should be dilated by a scale factor of 4 centered at the origin.

Based on the above information,

The figure should be proportional as the angle and the points should be the same. And, when the translation is done the image should be congruent to the pre-image

Therefore we can conclude that option d is correct.

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