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9. Dilate hexagon DEFGHI from center O using scale factor. D.

9. Dilate hexagon DEFGHI from center O using scale factor. D.

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.
### Geometric Transformations: Dilation of a Hexagon **Problem Statement:** Dilate hexagon DEFGHI from center O using scale factor . **Diagram Explanation:** In the given image, a hexagon labeled DEFGHI is shown, with a center point labeled O. This diagram serves to illustrate the process of dilating the hexagon from the center O. Dilation involves resizing the hexagon by a certain scale factor, where each vertex of the hexagon moves radially outward or inward from the center O based on the given scale factor. **Hexagon Coordinates:** - D - E - F - G - H - I - Center O Each vertex (D, E, F, G, H, I) will move along a line that extends from the center O to that vertex. The new position (D', E', F', G', H', I') of each vertex will be determined by the scale factor. For example, if the scale factor is 2, each vertex will move to a point that is twice as far from O as the original vertex. Conversely, if the scale factor is 1/2, each vertex will move to a point that is half as far from O as the original vertex. ### Steps to Dilate the Hexagon: 1. **Identify the Scale Factor:** Determine the given scale factor to apply in the transformation. 2. **Measure Distance from Center to Vertex:** Measure the distance from the center O to each of the vertices D, E, F, G, H, and I. 3. **Apply Scale Factor:** Multiply each of these distances by the scale factor. This will give you the distances from the center O to the new vertices D', E', F', G', H', and I'. 4. **Draw the New Hexagon:** Plot these new vertices using the calculated distances and connect them in the same order as the original hexagon. ### Example: Assuming the scale factor is 2, if the original distance from O to D is 3 units, the distance from O to the new vertex D' will be 6 units. Repeat this process for all vertices to complete the new hexagon. By following these steps, you can successfully dilate the hexagon DEFGHI from center O using the given scale factor. This method is applicable to any polygon and helps in understanding the concept of geometric transformations.
Transcribed Image Text:### Geometric Transformations: Dilation of a Hexagon **Problem Statement:** Dilate hexagon DEFGHI from center O using scale factor . **Diagram Explanation:** In the given image, a hexagon labeled DEFGHI is shown, with a center point labeled O. This diagram serves to illustrate the process of dilating the hexagon from the center O. Dilation involves resizing the hexagon by a certain scale factor, where each vertex of the hexagon moves radially outward or inward from the center O based on the given scale factor. **Hexagon Coordinates:** - D - E - F - G - H - I - Center O Each vertex (D, E, F, G, H, I) will move along a line that extends from the center O to that vertex. The new position (D', E', F', G', H', I') of each vertex will be determined by the scale factor. For example, if the scale factor is 2, each vertex will move to a point that is twice as far from O as the original vertex. Conversely, if the scale factor is 1/2, each vertex will move to a point that is half as far from O as the original vertex. ### Steps to Dilate the Hexagon: 1. **Identify the Scale Factor:** Determine the given scale factor to apply in the transformation. 2. **Measure Distance from Center to Vertex:** Measure the distance from the center O to each of the vertices D, E, F, G, H, and I. 3. **Apply Scale Factor:** Multiply each of these distances by the scale factor. This will give you the distances from the center O to the new vertices D', E', F', G', H', and I'. 4. **Draw the New Hexagon:** Plot these new vertices using the calculated distances and connect them in the same order as the original hexagon. ### Example: Assuming the scale factor is 2, if the original distance from O to D is 3 units, the distance from O to the new vertex D' will be 6 units. Repeat this process for all vertices to complete the new hexagon. By following these steps, you can successfully dilate the hexagon DEFGHI from center O using the given scale factor. This method is applicable to any polygon and helps in understanding the concept of geometric transformations.
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