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6. Use your compass and straightedge to construct AA'B'C' such that Dp 3(AABC) = AA'B'C'. %3D P.

6. Use your compass and straightedge to construct AA'B'C' such that Dp 3(AABC) = AA'B'C'. %3D P.

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.
### Construction of Triangle Using Compass and Straightedge #### Problem Statement: **6. Use your compass and straightedge to construct triangle \( \triangle A'B'C' \) such that \( D_{P,3}(\triangle ABC) = \triangle A'B'C' \).** #### Description: You are provided with an initial triangle \( \triangle ABC \) and a point \( P \) as shown in the diagram. The task is to construct a new triangle \( \triangle A'B'C' \) by performing a specific geometric transformation. #### Diagram Explanation: The diagram accompanying the problem consists of the following elements: - A triangle \( \triangle ABC \) with vertices labeled as \( A \), \( B \), and \( C \). - A point \( P \) outside the triangle \( \triangle ABC \). - The problem requires constructing a triangle \( \triangle A'B'C' \) such that it fulfills the condition \( D_{P,3}(\triangle ABC) = \triangle A'B'C' \). #### Steps for Construction: 1. **Identify Vertices:** Clearly mark the points \( A \), \( B \), and \( C \) on your paper. 2. **Draw Line Segments:** Using your straightedge, connect the points \( A \) to \( B \), \( B \) to \( C \), and \( C \) to \( A \) forming \( \triangle ABC \). 3. **Locate Point \( P \):** Place point \( P \) in the appropriate position as indicated in the diagram. 4. **Use Compass for Transformation:** - Set your compass width to a certain proportional distance (based on the specific conditions of the transformation \( D_{P,3} \)). - Rotate and translate each vertex of \( \triangle ABC \) with respect to point \( P \), preserving the specified relationship. 5. **Construct \( \triangle A'B'C' \):** - Mark the new vertices \( A' \), \( B' \), and \( C' \) at the determined locations after the transformation. - Connect these vertices using your straightedge to complete \( \triangle A'B'C' \). #### Understanding \( D_{P,3} \): - \( D_{P,3} \) represents a dilation of scale factor 3 centered at point \( P \). Ensure accuracy in each step to
Transcribed Image Text:### Construction of Triangle Using Compass and Straightedge #### Problem Statement: **6. Use your compass and straightedge to construct triangle \( \triangle A'B'C' \) such that \( D_{P,3}(\triangle ABC) = \triangle A'B'C' \).** #### Description: You are provided with an initial triangle \( \triangle ABC \) and a point \( P \) as shown in the diagram. The task is to construct a new triangle \( \triangle A'B'C' \) by performing a specific geometric transformation. #### Diagram Explanation: The diagram accompanying the problem consists of the following elements: - A triangle \( \triangle ABC \) with vertices labeled as \( A \), \( B \), and \( C \). - A point \( P \) outside the triangle \( \triangle ABC \). - The problem requires constructing a triangle \( \triangle A'B'C' \) such that it fulfills the condition \( D_{P,3}(\triangle ABC) = \triangle A'B'C' \). #### Steps for Construction: 1. **Identify Vertices:** Clearly mark the points \( A \), \( B \), and \( C \) on your paper. 2. **Draw Line Segments:** Using your straightedge, connect the points \( A \) to \( B \), \( B \) to \( C \), and \( C \) to \( A \) forming \( \triangle ABC \). 3. **Locate Point \( P \):** Place point \( P \) in the appropriate position as indicated in the diagram. 4. **Use Compass for Transformation:** - Set your compass width to a certain proportional distance (based on the specific conditions of the transformation \( D_{P,3} \)). - Rotate and translate each vertex of \( \triangle ABC \) with respect to point \( P \), preserving the specified relationship. 5. **Construct \( \triangle A'B'C' \):** - Mark the new vertices \( A' \), \( B' \), and \( C' \) at the determined locations after the transformation. - Connect these vertices using your straightedge to complete \( \triangle A'B'C' \). #### Understanding \( D_{P,3} \): - \( D_{P,3} \) represents a dilation of scale factor 3 centered at point \( P \). Ensure accuracy in each step to
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