5. Dor(A) = A' and Dor(B) = B'. Find the center of dilation, O, and the scale factor, r. %3D %3D A'0 O B' How does OA compare to 0A'? How does OB compare to OB'? a. b.
5. Dor(A) = A' and Dor(B) = B'. Find the center of dilation, O, and the scale factor, r. %3D %3D A'0 O B' How does OA compare to 0A'? How does OB compare to OB'? a. b.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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This is a geometry question.
![### Dilation and Scale Factor
**Problem 5**:
Given \(D_{O, r}(A) = A'\) and \(D_{O, r}(B) = B'\). Find the center of dilation, \(O\), and the scale factor, \(r\).
![Graph]
**Diagram**:
- The points \(A\) and \(A'\) are marked, indicating \(A'\) as the dilated image of \(A\).
- Similarly, the points \(B\) and \(B'\) are shown, with \(B'\) being the dilated image of \(B\).
**Questions:**
1. How does \(OA\) compare to \(OA'\)?
2. How does \(OB\) compare to \(OB'\)?
**Explanation**:
To solve this problem, follow these steps:
- Identify the center of dilation, \(O\).
- Measure the distances from \(O\) to \(A\), \(A'\), \(B\), and \(B'\).
- Determine the scale factor \(r\) by comparing the distances \(OA\) to \(OA'\) and \(OB\) to \(OB'\).
The scale factor \(r\) can be calculated using the formula:
\[ r = \frac{OA'}{OA} = \frac{OB'}{OB} \]
**Analytical Approach**:
- If \(OA = d\) and \(OA' = rd\), the dilation factor \(r\) indicates how much the object has been scaled.
- The relationships for any points \(A\) and \(B\) under the same dilation would also apply similarly.
**Answer the questions**:
1. \(OA'\) is \(r\) times \(OA\).
2. \(OB'\) is \(r\) times \(OB\).
This fundamental concept of dilation helps in understanding how objects scale relative to a point and a specific factor.
---
This transcribed and explained format makes the topic suitable for an educational website, ensuring clarity and aiding in the comprehension of the geometric concept of dilation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F15e8ee67-63a1-4f6c-9885-869f4fdcabb8%2F6b0d7c53-3f03-4ae4-afd0-92ff64ee17d6%2Fruus0l9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Dilation and Scale Factor
**Problem 5**:
Given \(D_{O, r}(A) = A'\) and \(D_{O, r}(B) = B'\). Find the center of dilation, \(O\), and the scale factor, \(r\).
![Graph]
**Diagram**:
- The points \(A\) and \(A'\) are marked, indicating \(A'\) as the dilated image of \(A\).
- Similarly, the points \(B\) and \(B'\) are shown, with \(B'\) being the dilated image of \(B\).
**Questions:**
1. How does \(OA\) compare to \(OA'\)?
2. How does \(OB\) compare to \(OB'\)?
**Explanation**:
To solve this problem, follow these steps:
- Identify the center of dilation, \(O\).
- Measure the distances from \(O\) to \(A\), \(A'\), \(B\), and \(B'\).
- Determine the scale factor \(r\) by comparing the distances \(OA\) to \(OA'\) and \(OB\) to \(OB'\).
The scale factor \(r\) can be calculated using the formula:
\[ r = \frac{OA'}{OA} = \frac{OB'}{OB} \]
**Analytical Approach**:
- If \(OA = d\) and \(OA' = rd\), the dilation factor \(r\) indicates how much the object has been scaled.
- The relationships for any points \(A\) and \(B\) under the same dilation would also apply similarly.
**Answer the questions**:
1. \(OA'\) is \(r\) times \(OA\).
2. \(OB'\) is \(r\) times \(OB\).
This fundamental concept of dilation helps in understanding how objects scale relative to a point and a specific factor.
---
This transcribed and explained format makes the topic suitable for an educational website, ensuring clarity and aiding in the comprehension of the geometric concept of dilation.
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