https://file.aiquickdraw.com/mathbot/file/17306967343717ex64thr.jpg

Based on the image, it appears that the problem involves finding the minimal length of an underground pipe that would connect two villages, labeled A and C, in a grid-like structure.

The problem setup:
1. Villages A, B, C, and D are represented on a grid.
2. The grid has points marked in blue and red, where red points represent obstacles that cannot be crossed.
3. We know that the distance between villages A and B is 9 km.

### Solution Approach:
1. **Determine the Scale:** Since the distance from A to B is given as 9 km, we can use this information to find the length represented by each unit on the grid. If the distance between A and B is 3 units on the grid, then each unit would be \( \frac{9}{3} = 3 \) km.
  
2. **Calculate the Straight-Line Distance:** To find the direct distance (using the Pythagorean theorem) between A and C, we need the horizontal and vertical distances in terms of units, then multiply by 3 km to convert to real distance.

3. **Distance Formula Application:**
   - If \( A \) is at coordinates \((x_1, y_1)\) and \( C \) at \((x_2, y_2)\) in grid units, the distance \( d \) is given by:
     \[
     d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
     \]
   - Convert the result into kilometers by multiplying by 3.

Once this calculation is complete, it will yield the minimum underground pipe length needed to connect A and C.

Would you like a detailed solution for each calculation step, or do you have any specific questions? 

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### Additional Questions:
1. How would we approach the problem if the obstacles were closer to A or C?
2. What if the grid distance between A and B was different? How would that affect our calculations?
3. How can this method be applied to other pairs of villages (e.g., A to D)?
4. If we had to avoid certain cells even for underground pipes, how would the calculation change?
5. Could a similar approach be used if there were more than four villages in a larger grid?

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**Tip:** When working with grids, always convert units according to the given scale before applying formulas for accurate results.

Gambar di bawah adalah peta jalan suatu kecamatan yang memuat desa A, B, C, dan D. Untuk mencapai suatu desa dari desa lainnya setiap kendaraan harus menggunakan jalan seperti pada gambar. Diketahui bahwa jarak desa A dan B adalah 9 km, serta titik-titiknya berwarna merah tidak dapat dilalui. Diketahui terdapat pipa air lurus dibawah tanah yang menghubungkan desa A dan C. Panjang minimal pipa tersebut adalah .... m

Learn how to find the minimum underground pipe length needed to connect villages A and C on a grid. The distance between villages A and B is given as 9 km, and obstacles prevent direct surface routes. This problem involves using coordinate geometry and the distance formula. Suitable for students in Grades 8-10.

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