G. А. 8/5 в. 4/17 С. 17

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
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### Geometry Problem: Calculating the Perimeter of Polygon DEFG

**Question:**
What is the perimeter of DEFG?

**Diagram:**
- The image presents a Cartesian coordinate system with grid lines and axis labels.
- Points D, E, F, and G form a quadrilateral. Their coordinates are:
  - D (3, 1)
  - E (2, 6)
  - F (6, 5)
  - G (5, 2)

**Answer Choices:**
A. \( 8\sqrt{5} \)

B. \( 4\sqrt{17} \)

C. 17

D. \( 4\sqrt{73} \)

**Explanation:**
To determine the perimeter of the polygon DEFG, calculate the distances between successive points using the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

1. **Distance DE:**
   \[
   \sqrt{(3 - 2)^2 + (1 - 6)^2} = \sqrt{1 + 25} = \sqrt{26}
   \]

2. **Distance EF:**
   \[
   \sqrt{(6 - 2)^2 + (5 - 6)^2} = \sqrt{16 + 1} = \sqrt{17}
   \]

3. **Distance FG:**
   \[
   \sqrt{(6 - 5)^2 + (5 - 2)^2} = \sqrt{1 + 9} = \sqrt{10}
   \]

4. **Distance GD:**
   \[
   \sqrt{(5 - 3)^2 + (2 - 1)^2} = \sqrt{4 + 1} = \sqrt{5}
   \]

Sum the distances to find the perimeter:
\[ \sqrt{26} + \sqrt{17} + \sqrt{10} + \sqrt{5} \]

Therefore, you need to evaluate the correct total perimeter based on these values, noting that the given answer choices suggest simplified forms.

Please choose the correct answer from the given options.
Transcribed Image Text:### Geometry Problem: Calculating the Perimeter of Polygon DEFG **Question:** What is the perimeter of DEFG? **Diagram:** - The image presents a Cartesian coordinate system with grid lines and axis labels. - Points D, E, F, and G form a quadrilateral. Their coordinates are: - D (3, 1) - E (2, 6) - F (6, 5) - G (5, 2) **Answer Choices:** A. \( 8\sqrt{5} \) B. \( 4\sqrt{17} \) C. 17 D. \( 4\sqrt{73} \) **Explanation:** To determine the perimeter of the polygon DEFG, calculate the distances between successive points using the distance formula: \[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] 1. **Distance DE:** \[ \sqrt{(3 - 2)^2 + (1 - 6)^2} = \sqrt{1 + 25} = \sqrt{26} \] 2. **Distance EF:** \[ \sqrt{(6 - 2)^2 + (5 - 6)^2} = \sqrt{16 + 1} = \sqrt{17} \] 3. **Distance FG:** \[ \sqrt{(6 - 5)^2 + (5 - 2)^2} = \sqrt{1 + 9} = \sqrt{10} \] 4. **Distance GD:** \[ \sqrt{(5 - 3)^2 + (2 - 1)^2} = \sqrt{4 + 1} = \sqrt{5} \] Sum the distances to find the perimeter: \[ \sqrt{26} + \sqrt{17} + \sqrt{10} + \sqrt{5} \] Therefore, you need to evaluate the correct total perimeter based on these values, noting that the given answer choices suggest simplified forms. Please choose the correct answer from the given options.
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