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Quadrilateral ABCD undergoes a dilation centered at A. The perimeter of AB'C'D' is 45. Determine the the scale factor of ABCD to AB'C'D' and compute the perimeter of ABCD.

Quadrilateral ABCD undergoes a dilation centered at A. The perimeter of AB'C'D' is 45. Determine the the scale factor of ABCD to AB'C'D' and compute the perimeter of ABCD.

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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**Question 2:** Quadrilateral \(ABCD\) undergoes a dilation centered at \(A\). The perimeter of \(ABC'D'\) is 45. Determine the scale factor of \(ABCD\) to \(ABC'D'\) and compute the perimeter of \(ABCD\). - **A:** Scale factor = 3, perimeter = 15 - **B:** Scale factor = \(\frac{1}{3}\), perimeter = 135 - **C:** Scale factor = \(\frac{3}{2}\), perimeter = 30 - **D:** Scale factor = 2, perimeter = 22.5 **Diagram Explanation:** The diagram shows a quadrilateral \(ABCD\) and its dilated image \(ABC'D'\). Point \(A\) is the center of dilation. The lines \(BB'\) and \(CC'\) indicate the directions of the dilation. The lengths indicated in the diagram are \(6\) and \(9\), relevant to the positions of the points involved. **©2020 Illuminate Education™, Inc.**
Transcribed Image Text:**Question 2:** Quadrilateral \(ABCD\) undergoes a dilation centered at \(A\). The perimeter of \(ABC'D'\) is 45. Determine the scale factor of \(ABCD\) to \(ABC'D'\) and compute the perimeter of \(ABCD\). - **A:** Scale factor = 3, perimeter = 15 - **B:** Scale factor = \(\frac{1}{3}\), perimeter = 135 - **C:** Scale factor = \(\frac{3}{2}\), perimeter = 30 - **D:** Scale factor = 2, perimeter = 22.5 **Diagram Explanation:** The diagram shows a quadrilateral \(ABCD\) and its dilated image \(ABC'D'\). Point \(A\) is the center of dilation. The lines \(BB'\) and \(CC'\) indicate the directions of the dilation. The lengths indicated in the diagram are \(6\) and \(9\), relevant to the positions of the points involved. **©2020 Illuminate Education™, Inc.**
**Question 3** The line with the equation undergoes a dilation with a scale factor of 2 and the center at (0,0). Which equation describes the line that is the result of this dilation? - A - B - C - D --- *Note: The original equation of the line is not provided in the image. When undergoing dilation centered at the origin, the slope of the line remains unchanged, but you would generally multiply the distance of every point on the line from the origin by the scale factor.*
Transcribed Image Text:**Question 3** The line with the equation undergoes a dilation with a scale factor of 2 and the center at (0,0). Which equation describes the line that is the result of this dilation? - A - B - C - D --- *Note: The original equation of the line is not provided in the image. When undergoing dilation centered at the origin, the slope of the line remains unchanged, but you would generally multiply the distance of every point on the line from the origin by the scale factor.*
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