Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Ask your questions and receive precise answers from experienced professionals across different disciplines. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
To determine which composition of similarity transformations maps polygon [tex]\( ABCD \)[/tex] to polygon [tex]\( A'B'C'D' \)[/tex], we should evaluate the options given:
1. A dilation with a scale factor of [tex]\(\frac{1}{4}\)[/tex] and then a rotation:
- A dilation with a scale factor of [tex]\(\frac{1}{4}\)[/tex] would reduce the size of the polygon to one-fourth of its original size.
- Following the dilation, performing a rotation would rotate the already reduced-sized polygon by a certain angle around a fixed point. This does not involve any shifting of the position other than the rotational shift.
2. A dilation with a scale factor of [tex]\(\frac{1}{4}\)[/tex] and then a translation:
- Similarly, a dilation with a scale factor of [tex]\(\frac{1}{4}\)[/tex] would reduce the size of the polygon.
- Following the dilation, performing a translation would move (or shift) the entire reduced-sized polygon to a different location without changing its orientation.
3. A dilation with a scale factor of 4 and then a rotation:
- A dilation with a scale factor of 4 would increase the size of the polygon to four times its original size.
- Following the dilation, performing a rotation rotates the larger polygon around a fixed point. This also does not involve any shifting of the position other than the rotational shift.
4. A dilation with a scale factor of 4 and then a translation:
- A dilation with a scale factor of 4 would increase the size of the polygon to four times its original size.
- Following the dilation, performing a translation shifts (or moves) the entire larger polygon to a different location without changing its orientation.
Given that the correct composition of transformations is a dilation with a scale factor of 4 and then a translation, it means we are looking at option 4:
- The polygon [tex]\(ABCD\)[/tex] is first enlarged by a factor of 4 to become 4 times its original size.
- Then, the newly resized polygon is translated, which means moved to a different position without altering its orientation.
Thus, the appropriate composition of similarity transformations that maps polygon [tex]\(ABCD\)[/tex] to polygon [tex]\(A'B'C'D'\)[/tex] is:
A dilation with a scale factor of 4 and then a translation.
1. A dilation with a scale factor of [tex]\(\frac{1}{4}\)[/tex] and then a rotation:
- A dilation with a scale factor of [tex]\(\frac{1}{4}\)[/tex] would reduce the size of the polygon to one-fourth of its original size.
- Following the dilation, performing a rotation would rotate the already reduced-sized polygon by a certain angle around a fixed point. This does not involve any shifting of the position other than the rotational shift.
2. A dilation with a scale factor of [tex]\(\frac{1}{4}\)[/tex] and then a translation:
- Similarly, a dilation with a scale factor of [tex]\(\frac{1}{4}\)[/tex] would reduce the size of the polygon.
- Following the dilation, performing a translation would move (or shift) the entire reduced-sized polygon to a different location without changing its orientation.
3. A dilation with a scale factor of 4 and then a rotation:
- A dilation with a scale factor of 4 would increase the size of the polygon to four times its original size.
- Following the dilation, performing a rotation rotates the larger polygon around a fixed point. This also does not involve any shifting of the position other than the rotational shift.
4. A dilation with a scale factor of 4 and then a translation:
- A dilation with a scale factor of 4 would increase the size of the polygon to four times its original size.
- Following the dilation, performing a translation shifts (or moves) the entire larger polygon to a different location without changing its orientation.
Given that the correct composition of transformations is a dilation with a scale factor of 4 and then a translation, it means we are looking at option 4:
- The polygon [tex]\(ABCD\)[/tex] is first enlarged by a factor of 4 to become 4 times its original size.
- Then, the newly resized polygon is translated, which means moved to a different position without altering its orientation.
Thus, the appropriate composition of similarity transformations that maps polygon [tex]\(ABCD\)[/tex] to polygon [tex]\(A'B'C'D'\)[/tex] is:
A dilation with a scale factor of 4 and then a translation.
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.
