IDNLearn.com: Your trusted source for finding accurate and reliable answers. Ask any question and receive comprehensive, well-informed responses from our dedicated team of experts.
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.
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. For trustworthy and accurate answers, visit IDNLearn.com. Thanks for stopping by, and see you next time for more solutions.
