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Write the inverse transformation for each of the following so that the composition of the transformation with its 2. inverse maps a point to itself on the plane. a. T b. REAS C. d. Dor

Write the inverse transformation for each of the following so that the composition of the transformation with its 2. inverse maps a point to itself on the plane. a. T b. REAS C. d. Dor

Elementary Geometry For College Students, 7e
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. Only problem 2 please.
### Dilations and Inverse Transformations **1. Understanding Dilations:** On the diagram below, \( O \) is a center of dilation, and \( \overline{AD} \) is a line not through \( O \). Choose two points \( B \) and \( C \) on \( \overline{AD} \) between \( A \) and \( D \). #### Diagram Explanation: - The diagram shows three points \( A \), \( B \), \( C \), and \( D \) on a line segment with point \( O \) not lying on the line segment. #### Instructions: a. **Dilate \( A, B, C, \) and \( D \) from \( O \) using scale factor \( r = \frac{1}{2} \). Label the images \( A', B', C', \) and \( D' \), respectively.** b. **Dilate \( A, B, C, \) and \( D \) from \( O \) using scale factor \( r = 2 \). Label the images \( A'', B'', C'', \) and \( D'' \), respectively.** c. **Dilate \( A, B, C, \) and \( D \) from \( O \) using scale factor \( r = 3 \). Label the images \( A''', B''', C''', \) and \( D''' \), respectively.** d. **Draw a conclusion about the effect of a dilation on a line segment based on the diagram that you drew. Explain.** **2. Inverse Transformations:** Write the inverse transformation for each of the following so that the composition of the transformation with its inverse maps a point to itself on the plane. a. \( T_{AB} \) b. \( r_{AB} \) c. \( R_{C,45} \) d. \( D_{O,r} \) ### Graph/Diagram Analysis: 1. The diagram illustrates a linear segment \( \overline{AD} \) with points \( A, B, C, \) and \( D \) marked along it. Point \( O \) is plotted off this line segment. 2. For each dilation task: - Points \( A, B, C, \) and \( D \) will be transformed according to the specified scale factor. - The images of
Transcribed Image Text:### Dilations and Inverse Transformations **1. Understanding Dilations:** On the diagram below, \( O \) is a center of dilation, and \( \overline{AD} \) is a line not through \( O \). Choose two points \( B \) and \( C \) on \( \overline{AD} \) between \( A \) and \( D \). #### Diagram Explanation: - The diagram shows three points \( A \), \( B \), \( C \), and \( D \) on a line segment with point \( O \) not lying on the line segment. #### Instructions: a. **Dilate \( A, B, C, \) and \( D \) from \( O \) using scale factor \( r = \frac{1}{2} \). Label the images \( A', B', C', \) and \( D' \), respectively.** b. **Dilate \( A, B, C, \) and \( D \) from \( O \) using scale factor \( r = 2 \). Label the images \( A'', B'', C'', \) and \( D'' \), respectively.** c. **Dilate \( A, B, C, \) and \( D \) from \( O \) using scale factor \( r = 3 \). Label the images \( A''', B''', C''', \) and \( D''' \), respectively.** d. **Draw a conclusion about the effect of a dilation on a line segment based on the diagram that you drew. Explain.** **2. Inverse Transformations:** Write the inverse transformation for each of the following so that the composition of the transformation with its inverse maps a point to itself on the plane. a. \( T_{AB} \) b. \( r_{AB} \) c. \( R_{C,45} \) d. \( D_{O,r} \) ### Graph/Diagram Analysis: 1. The diagram illustrates a linear segment \( \overline{AD} \) with points \( A, B, C, \) and \( D \) marked along it. Point \( O \) is plotted off this line segment. 2. For each dilation task: - Points \( A, B, C, \) and \( D \) will be transformed according to the specified scale factor. - The images of
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