Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
To determine the scale factor by which line segment [tex]\(\overline{AB}\)[/tex] was dilated to create [tex]\(\overline{A'B'}\)[/tex], we'll follow these steps:
1. Identify the coordinates of [tex]\(A'\)[/tex] and [tex]\(B'\)[/tex]:
- [tex]\(A'(0, 4)\)[/tex]
- [tex]\(B'(4, 6)\)[/tex]
2. Calculate the distance from the origin (0,0) to [tex]\(A'\)[/tex]:
[tex]\[ \text{Distance from origin to } A' = \sqrt{(0-0)^2 + (4-0)^2} = \sqrt{0 + 16} = \sqrt{16} = 4 \][/tex]
3. Calculate the distance from the origin (0,0) to [tex]\(B'\)[/tex]:
[tex]\[ \text{Distance from origin to } B' = \sqrt{(4-0)^2 + (6-0)^2} = \sqrt{16 + 36} = \sqrt{52} \approx 7.211 \][/tex]
4. Determine the scale factor:
- The scale factor [tex]\(k\)[/tex] can be found by dividing the distance from the origin to [tex]\(B'\)[/tex] by the distance from the origin to [tex]\(A'\)[/tex]:
[tex]\[ k = \frac{\text{Distance from origin to } B'}{\text{Distance from origin to } A'} = \frac{7.211}{4} \approx 1.803 \][/tex]
Thus, the scale factor [tex]\(k\)[/tex] by which [tex]\(\overline{AB}\)[/tex] was dilated to create [tex]\(\overline{A'B'}\)[/tex] is approximately 1.803. Therefore, the correct scale factor closest to this value in the given options is:
[tex]\[ \boxed{2} \][/tex]
1. Identify the coordinates of [tex]\(A'\)[/tex] and [tex]\(B'\)[/tex]:
- [tex]\(A'(0, 4)\)[/tex]
- [tex]\(B'(4, 6)\)[/tex]
2. Calculate the distance from the origin (0,0) to [tex]\(A'\)[/tex]:
[tex]\[ \text{Distance from origin to } A' = \sqrt{(0-0)^2 + (4-0)^2} = \sqrt{0 + 16} = \sqrt{16} = 4 \][/tex]
3. Calculate the distance from the origin (0,0) to [tex]\(B'\)[/tex]:
[tex]\[ \text{Distance from origin to } B' = \sqrt{(4-0)^2 + (6-0)^2} = \sqrt{16 + 36} = \sqrt{52} \approx 7.211 \][/tex]
4. Determine the scale factor:
- The scale factor [tex]\(k\)[/tex] can be found by dividing the distance from the origin to [tex]\(B'\)[/tex] by the distance from the origin to [tex]\(A'\)[/tex]:
[tex]\[ k = \frac{\text{Distance from origin to } B'}{\text{Distance from origin to } A'} = \frac{7.211}{4} \approx 1.803 \][/tex]
Thus, the scale factor [tex]\(k\)[/tex] by which [tex]\(\overline{AB}\)[/tex] was dilated to create [tex]\(\overline{A'B'}\)[/tex] is approximately 1.803. Therefore, the correct scale factor closest to this value in the given options is:
[tex]\[ \boxed{2} \][/tex]
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.