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A size transformation centered at some point O on line m takes a point P onto P'. Explain how to draw (a) the center O of the transformation and (b) the image Q' of the point Q, where Q lies on m. P'. P. ..... O A. The line PP' passes through O, so constructing this line, along with line m, determines point O. PQ and P'Q' are parallel, so the line through P' that is parallel to PQ will meet line m at the desired point Q' O B. PQ and P'O are parallel, so the line through P' that is parallel to PQ will determine O. The line PP' passes through Q', so constructing this line determines point Q'. OC. The line PP' passes through O, so constructing this line determines point O. The line OQ passes through Q', so constructing this line determines the point Q'. O D. PQ and P'O are parallel, so the line through P' that is parallel to PQ will determine O. The line OQ passes through Q', so constructing this line determines the point Q'.

A size transformation centered at some point O on line m takes a point P onto P'. Explain how to draw (a) the center O of the transformation and (b) the image Q' of the point Q, where Q lies on m. P'. P. ..... O A. The line PP' passes through O, so constructing this line, along with line m, determines point O. PQ and P'Q' are parallel, so the line through P' that is parallel to PQ will meet line m at the desired point Q' O B. PQ and P'O are parallel, so the line through P' that is parallel to PQ will determine O. The line PP' passes through Q', so constructing this line determines point Q'. OC. The line PP' passes through O, so constructing this line determines point O. The line OQ passes through Q', so constructing this line determines the point Q'. O D. PQ and P'O are parallel, so the line through P' that is parallel to PQ will determine O. The line OQ passes through Q', so constructing this line determines the point Q'.

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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**Title: Understanding Size Transformations: A Step-by-Step Guide** **Description:** This educational module explains how to perform a size transformation centered at a point O on a line m, taking a point P onto P′. The key steps involved are determining the center O and the transformed point Q′ for a point Q that lies on line m. **Instructions:** 1. **Objective:** Explain how to draw: - (a) The center O of the transformation. - (b) The image Q′ of point Q, where Q lies on line m. 2. **Diagram Explanation:** - The diagram shows point P on line m, being transformed to P′. A line m is indicated, passing through point Q. 3. **Options for Explanation:** - **A.** The line PP′ passes through O, so constructing this line, along with line m, determines point O. \( \overline{PQ} \) and \( \overline{P'Q'} \) are parallel, so the line through P′ that is parallel to \( \overline{PQ} \) will meet line m at the desired point Q′. - **B.** \( \overline{PQ} \) and \( \overline{P'O} \) are parallel, so the line through P′ that is parallel to \( \overline{PQ} \) will determine O. The line PP′ passes through Q′, so constructing this line determines point Q′. - **C.** The line PP′ passes through O, so constructing this line determines point O. The line OQ passes through Q′, so constructing this line determines the point Q′. - **D.** \( \overline{PQ} \) and \( \overline{P'O} \) are parallel, so the line through P′ that is parallel to \( \overline{PQ} \) will determine O. The line OQ passes through Q′, so constructing this line determines the point Q′. **Conclusion:** Using the above methods, learners can understand how to perform a size transformation by accurately determining the center and transformed points on a given line. This exercise aids in grasping fundamental concepts of geometry transformations.
Transcribed Image Text:**Title: Understanding Size Transformations: A Step-by-Step Guide** **Description:** This educational module explains how to perform a size transformation centered at a point O on a line m, taking a point P onto P′. The key steps involved are determining the center O and the transformed point Q′ for a point Q that lies on line m. **Instructions:** 1. **Objective:** Explain how to draw: - (a) The center O of the transformation. - (b) The image Q′ of point Q, where Q lies on line m. 2. **Diagram Explanation:** - The diagram shows point P on line m, being transformed to P′. A line m is indicated, passing through point Q. 3. **Options for Explanation:** - **A.** The line PP′ passes through O, so constructing this line, along with line m, determines point O. \( \overline{PQ} \) and \( \overline{P'Q'} \) are parallel, so the line through P′ that is parallel to \( \overline{PQ} \) will meet line m at the desired point Q′. - **B.** \( \overline{PQ} \) and \( \overline{P'O} \) are parallel, so the line through P′ that is parallel to \( \overline{PQ} \) will determine O. The line PP′ passes through Q′, so constructing this line determines point Q′. - **C.** The line PP′ passes through O, so constructing this line determines point O. The line OQ passes through Q′, so constructing this line determines the point Q′. - **D.** \( \overline{PQ} \) and \( \overline{P'O} \) are parallel, so the line through P′ that is parallel to \( \overline{PQ} \) will determine O. The line OQ passes through Q′, so constructing this line determines the point Q′. **Conclusion:** Using the above methods, learners can understand how to perform a size transformation by accurately determining the center and transformed points on a given line. This exercise aids in grasping fundamental concepts of geometry transformations.
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