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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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Could I please get help
### Ratio Calculation

To find the ratio of \(\dfrac{A'B'}{AB}\):

#### Diagram Explanation
There is a coordinate graph where:
- A is positioned at (2, 2),
- B is positioned at (4, 2),
- A' is positioned at (2, 6),
- B' is positioned at (9, 3),
- C is positioned at (4, 6),
- C' is positoned at (10, 10).

#### Steps to Calculate the Ratio
1. Determine the length of segment \(AB\):
    - A (2, 2) to B (4, 2)
    - The difference in x-coordinates: \(4 - 2 = 2\).
    - Since both points share the same y-coordinate, the length of \(AB\) is 2 units.

2. Determine the length of segment \(A'B'\):
    - A' (2, 6) to B' (9, 3)
    - Using the distance formula: \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
    - \(\sqrt{(9 - 2)^2 + (3 - 6)^2} = \sqrt{7^2 + (-3)^2} = \sqrt{49 + 9} = \sqrt{58}\).

3. Find the ratio \(\dfrac{A'B'}{AB}\):
    - \(\dfrac{\sqrt{58}}{2}\)

The options provided are:
- 2
- 3
- 6
- 12

Based on our more detailed calculation, none of the given options match the exact calculation of the ratio. Double-check calculations and graph plotted points for more precision.
Transcribed Image Text:### Ratio Calculation To find the ratio of \(\dfrac{A'B'}{AB}\): #### Diagram Explanation There is a coordinate graph where: - A is positioned at (2, 2), - B is positioned at (4, 2), - A' is positioned at (2, 6), - B' is positioned at (9, 3), - C is positioned at (4, 6), - C' is positoned at (10, 10). #### Steps to Calculate the Ratio 1. Determine the length of segment \(AB\): - A (2, 2) to B (4, 2) - The difference in x-coordinates: \(4 - 2 = 2\). - Since both points share the same y-coordinate, the length of \(AB\) is 2 units. 2. Determine the length of segment \(A'B'\): - A' (2, 6) to B' (9, 3) - Using the distance formula: \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\) - \(\sqrt{(9 - 2)^2 + (3 - 6)^2} = \sqrt{7^2 + (-3)^2} = \sqrt{49 + 9} = \sqrt{58}\). 3. Find the ratio \(\dfrac{A'B'}{AB}\): - \(\dfrac{\sqrt{58}}{2}\) The options provided are: - 2 - 3 - 6 - 12 Based on our more detailed calculation, none of the given options match the exact calculation of the ratio. Double-check calculations and graph plotted points for more precision.
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