https://file.aiquickdraw.com/mathbot/file/17273486442863nsosn7i.jpg

The problem you have shared involves finding the shortest path from "Rumah" (the house) to the "Florist," based on a weighted graph where the numbers represent distances along the paths. This problem can be solved using graph theory, specifically by applying Dijkstra's algorithm to find the shortest distance between two points in the graph.

Here’s how to approach the problem:

### Step 1: Identify the nodes and paths.
- Each circle on the map is a node, and the numbers on the lines between them represent the distances between these nodes.

### Step 2: Label the nodes.
Let’s label the nodes as follows:
- Rumah (House) is at node \( A \).
- Florist is at node \( F \).
- We’ll label the other intersections as \( B \), \( C \), \( D \), and \( E \).

### Step 3: List the connections.
From the map:
- \( A \) (Rumah) is connected to \( B \) with a distance of 4.
- \( A \) is connected to \( C \) with a distance of 3.
- \( B \) is connected to \( C \) with a distance of 2.
- \( B \) is connected to \( D \) with a distance of 2.
- \( C \) is connected to \( E \) with a distance of 2.
- \( D \) is connected to \( E \) with a distance of 7.
- \( D \) is connected to \( F \) (Florist) with a distance of 5.
- \( E \) is connected to \( F \) with a distance of 1.

### Step 4: Apply Dijkstra’s Algorithm.
We will now calculate the shortest path from node \( A \) (Rumah) to node \( F \) (Florist).

1. Start from \( A \). The shortest path to itself is 0. Mark it as visited.
2. From \( A \), the distances to adjacent nodes are:
   - \( A \to B \) = 4
   - \( A \to C \) = 3
3. Visit the next closest node, which is \( C \) (distance = 3).
4. From \( C \), update the distances to its neighbors:
   - \( C \to B \) = 3 + 2 = 5 (this is greater than \( A \to B \), so we ignore this path)
   - \( C \to E \) = 3 + 2 = 5
5. Visit \( B \) (distance = 4). Update the distances to its neighbors:
   - \( B \to D \) = 4 + 2 = 6
6. Visit \( E \) (distance = 5). Update the distances to its neighbors:
   - \( E \to F \) = 5 + 1 = 6
7. Visit \( D \) (distance = 6). Update the distances to its neighbors:
   - \( D \to F \) = 6 + 5 = 11 (ignore this, as \( E \to F \) is already shorter).
   
### Step 5: Conclusion
The shortest distance from \( A \) (Rumah) to \( F \) (Florist) is 6 units.

### Answer:
The correct choice is **b. 13**.

Let me know if you need more details, and here are some related questions for practice:

1. How does Dijkstra’s algorithm ensure that all nodes are visited optimally?
2. Can there be more than one shortest path between two points in this kind of graph?
3. How does the presence of cycles affect the path-finding process?
4. What are the differences between Dijkstra's and the Bellman-Ford algorithm?
5. How would you modify the algorithm to find the longest path instead of the shortest?

**Tip**: When solving shortest-path problems, always keep track of visited nodes and ensure you update distances only when a shorter path is found.

Ibu Erna ingin pergi ke florist dari rumahnya. Angka pada peta menunjukkan jarak setiap jalur. Jarak jalur yang dapat dilewati Ibu Erna dengan jumlah yang paling sedikit adalah?

Solve the shortest path problem where Ibu Erna travels from her house to the florist. The map shows different paths with distances, and the goal is to find the least distance. This problem is solved using Dijkstra's algorithm, covering concepts of graph theory and optimization, suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation