https://file.aiquickdraw.com/mathbot/file/1727345436231wnc7k97r.jpg

The problem asks which of the provided maps is **connected**. In graph theory, a map is connected if there is a path between any two points (or nodes) on the map, meaning that it's possible to travel between any pair of points without leaving the map.

Let’s evaluate the four maps:

- **Map A**: There are five points (A, B, C, D, E). All of them are connected through paths, either directly or indirectly. You can reach any point from any other point.
- **Map B**: There are three points (A, B, C), but there is no path between point A and either point B or C, so this map is not connected.
- **Map C**: Points A, B, C, and D are connected, but point E is isolated with no paths leading to it. Therefore, this map is not fully connected.
- **Map D**: There are four points (A, B, C, D), but the river divides the map into two separate regions. Points A and B are on one side, and points C and D are on the other side, so this map is also not connected.

### Conclusion:
- **Map A** is the only connected map.

Would you like further details or explanations on connected graphs?

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Here are some related questions:
1. What is the formal definition of a connected graph in topology or graph theory?
2. How do you determine if a graph is connected when visualizing it?
3. Can a graph be partially connected? If so, what is it called?
4. What are the practical applications of connected graphs in real-world mapping?
5. How does a river or barrier affect connectivity in map problems?

**Tip**: When analyzing connected graphs, always ensure that every node is reachable from every other node through some path, either directly or indirectly.

Which of the following maps is connected?

Understand how to identify connected graphs in map problems, using concepts from graph theory. Learn which of the provided maps is connected and why, with a step-by-step breakdown of connectivity and graph components. Suitable for high school students learning graph theory.

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