Question

Which of the following describes the image of a triangle after a dilation that has a scale factor of 2/3?
A.-Each angle has 2/3 of the measure of its corresponding angle in the pre-image
B.-Each side has the same measure as its corresponding angle in the pre-image.
C.-Each angle has the same measure as its corresponding angle in the pre-image.
D.-Each side has 3/2 the length of its corresponding length in the pre-image.

Answer 1

We want to see which statement describes the image of a triangle after a dilation of scale factor of 2/3.

We will see that the correct option is C:

"Each angle has the same measure as its corresponding angle in the pre-image."

First, if we have a given figure and we apply a dilation of scale factor K, then all the measures of the given figures are affected by that dilation.

So if the 3 sides of the original triangle measured A, B, and C.

The new measures will be:

• C' = k*C
• B' = k*B
• A' = k*A

Notice that because all the sides changed proportionally, then the internal angles produced did not change after the dilation.

From this, we can conclude that the only correct option is C:

"Each angle has the same measure as its corresponding angle in the pre-image."

This says that the angles of the dilated triangle are the same ones as the angles of the initial triangle, which is true.

If you want to learn more, you can read:

https://brainly.com/question/18605984