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The question is asking to determine which of the given polygons (A, B, or C) has the largest perimeter. The coordinates for each polygon's vertices are provided. To solve this, we need to calculate the perimeter for each polygon using the distance formula between consecutive points.

The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

### Coordinates:

- **Polygon A (ABCDE):**
  - A(2, 7)
  - B(2, 4)
  - C(4, 2)
  - D(6, 4)
  - E(4, 7)

- **Polygon B (EFG):**
  - E(-2, 2)
  - F(-3, -3)
  - G(4, -1)

- **Polygon C (HIJK):**
  - H(2, -3)
  - I(5, -5)
  - J(9, -5)
  - K(6, -1)

Let me calculate the distances and perimeters for each polygon.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like me to guide you through the steps so you can calculate the perimeters manually? Feel free to ask for more details or any other questions.

Here are some related questions you might find interesting:

1. What is the formula for calculating the area of a polygon given its vertices?
2. How do you determine if a polygon is convex or concave?
3. What is the significance of the perimeter in practical applications?
4. Can we use a different method to calculate perimeters for irregular polygons?
5. How would you compute the perimeter of a circle or an ellipse?

**Tip:** When calculating distances between points, always double-check the coordinates to avoid errors in the formula.

En cada caso los puntos determinan los vértices de un polígono, determine cuál de los polígonos tiene mayor perímetro. A. POLÍGONO ABCDE: {A (2,7); B (2,4); C (4,2); D (6,4); E (4,7)}. B. POLÍGONO EFG: {E (-2,2); F (-3,-3); G (4,-1)}. C. POLÍGONO HIJK: {H (2,-3); I (5,-5); J (9,-5); K (6,-1)}

This problem involves calculating the perimeters of three polygons, given their vertices' coordinates. You will apply the distance formula and basic geometry concepts to determine which polygon (ABCDE, EFG, or HIJK) has the largest perimeter. Perfect for students in Grades 9-12 learning about geometry and perimeter calculations.

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