https://file.aiquickdraw.com/mathbot/file/17261911508126fiqh9cg.jpg

For part **c)** of the exercise, let's analyze the situation:

### c) 
**La casa de Juanita está a la misma distancia de las escuelas A, C y D.**
- **i. ¿Dónde vive Juanita?**

Since Juanita's house is equidistant from schools A, C, and D, her location must be on the **circumcenter** of the triangle formed by these three points. The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect, and it is equidistant from all three vertices.

We can identify the circumcenter by calculating or by visually analyzing the Voronoi diagram. Based on the diagram, Juanita lives at the **intersection of the regions** for schools A, C, and D.

- **ii. ¿Qué tan lejos vive Juanita de cada una de estas escuelas?**

Once we determine Juanita's coordinates, we can use the distance formula to find her distance from each school. Since her house is equidistant from schools A, C, and D, we only need to calculate the distance once.

Let’s outline the approach:

- We need to **identify the coordinates** of the circumcenter of the triangle formed by the schools A, C, and D. Based on the graph, the circumcenter appears to be near \((2, 4)\), but we would need to confirm this.
  
- Once we have Juanita’s position, we apply the distance formula:
  \[
  d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
  \]
  to calculate the distance between her house and one of the schools (say, school A). Since she is equidistant from all three schools, this same distance will apply to the other schools as well.

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Do you want help calculating the exact circumcenter or distances? Let me know!

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### Related questions:
1. How do we calculate the circumcenter of a triangle?
2. What properties does the circumcenter of a triangle have?
3. What are Voronoi diagrams used for in mathematics and real-world applications?
4. How can we find the perpendicular bisectors of a triangle's sides geometrically?
5. How does the distance formula help in geometric problems?

### Tip:
The circumcenter of a triangle is always equidistant from all three vertices, making it a useful concept for problems involving distances.

This math problem asks to find the location of Juanita's house, which is equidistant from three schools (A, C, and D) using Voronoi diagrams and the concept of a triangle's circumcenter. Suitable for students in Grades 10-12, this problem involves geometric analysis and the distance formula.

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