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Analyze the dilation below. What can be determined about the scale factor?

Analyze the dilation below. What can be determined about the scale factor?

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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Analyze the dilation below. What can be determined about the scale factor?

**Graph Analysis** The graph presents a coordinate grid with two rectangles: rectangle ABCD (in red) and rectangle A'B'C'D' (in blue). The origin is at (0,0). **Rectangle ABCD (Red):** - Points: A (2,3), B (5,3), C (5,1), D (2,1) - Dimensions: Width = 3 units (from x=2 to x=5), Height = 2 units (from y=1 to y=3) **Rectangle A'B'C'D' (Blue):** - Points: A' (4,6), B' (10,6), C' (10,2), D' (4,2) - Dimensions: Width = 6 units (from x=4 to x=10), Height = 4 units (from y=2 to y=6) **Dilation Analysis:** The blue rectangle A'B'C'D' is a dilation of the red rectangle ABCD. By comparing the dimensions: - The width of ABCD (3 units) dilates to A'B'C'D' (6 units). - The height of ABCD (2 units) dilates to A'B'C'D' (4 units). **Scale Factor:** The scale factor is determined by dividing the dimensions of A'B'C'D' by the dimensions of ABCD. Both width and height scale by a factor of 2 (6/3 = 2 and 4/2 = 2). Thus, the scale factor is 2. This means rectangle ABCD is enlarged by a scale factor of 2 to form rectangle A'B'C'D'.
Transcribed Image Text:**Graph Analysis** The graph presents a coordinate grid with two rectangles: rectangle ABCD (in red) and rectangle A'B'C'D' (in blue). The origin is at (0,0). **Rectangle ABCD (Red):** - Points: A (2,3), B (5,3), C (5,1), D (2,1) - Dimensions: Width = 3 units (from x=2 to x=5), Height = 2 units (from y=1 to y=3) **Rectangle A'B'C'D' (Blue):** - Points: A' (4,6), B' (10,6), C' (10,2), D' (4,2) - Dimensions: Width = 6 units (from x=4 to x=10), Height = 4 units (from y=2 to y=6) **Dilation Analysis:** The blue rectangle A'B'C'D' is a dilation of the red rectangle ABCD. By comparing the dimensions: - The width of ABCD (3 units) dilates to A'B'C'D' (6 units). - The height of ABCD (2 units) dilates to A'B'C'D' (4 units). **Scale Factor:** The scale factor is determined by dividing the dimensions of A'B'C'D' by the dimensions of ABCD. Both width and height scale by a factor of 2 (6/3 = 2 and 4/2 = 2). Thus, the scale factor is 2. This means rectangle ABCD is enlarged by a scale factor of 2 to form rectangle A'B'C'D'.
Below is a multiple-choice question related to determining a scale factor: - The scale factor cannot be determined. - The scale factor is less than 1. - The scale factor is equal to 1. - The scale factor is greater than 1.
Transcribed Image Text:Below is a multiple-choice question related to determining a scale factor: - The scale factor cannot be determined. - The scale factor is less than 1. - The scale factor is equal to 1. - The scale factor is greater than 1.
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