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The above figure shows two-dimensional view of a city region. The various lines (A, B, C, D) represent paths taken by different people walking in the city. All blocks are 120 m on a side. What is the magnitude of the displacement from start to finish for path B? Express only the number of your answer in m.

From the image provided, we can see that path B follows a series of vertical and horizontal movements through a grid. All blocks are 120 m on each side, and the problem asks for the magnitude of the displacement from the start to the end for path B.

Here’s a step-by-step breakdown:

1. **Identify Start and End Positions for Path B**:
   - Path B starts near point D and makes movements through the grid.
   - We need to focus on the straight-line distance between the start and end points for displacement (ignoring the actual path taken).

2. **Horizontal and Vertical Movement**:
   - Since all blocks are 120 meters on each side, we can count the number of blocks moved horizontally and vertically to calculate the total displacement.
   - Horizontal and vertical movements can be treated as the legs of a right triangle.

3. **Apply the Pythagorean Theorem**:
   - Displacement = \(\sqrt{(horizontal \, distance)^2 + (vertical \, distance)^2}\)

Let me analyze the number of blocks for the horizontal and vertical distances in path B and calculate the total displacement.The magnitude of the displacement from the start to the finish for path B is \(600\) meters.

Would you like further details or have any questions? Here are some related questions for further exploration:

1. How do we calculate the displacement for other paths like A or C?
2. What is the difference between displacement and distance traveled?
3. How would the displacement change if the city blocks were not uniform?
4. How can vector addition be used to compute displacements in city grids?
5. What other real-world scenarios involve calculating displacements like this?

**Tip:** Displacement is always the straight-line distance between the starting and ending points, regardless of the path taken.

Solve the problem of calculating the magnitude of displacement for path B in a city grid. Each block is 120 meters on a side, and we use the Pythagorean Theorem to compute the straight-line distance between the start and finish. Suitable for students in Grades 7-9.

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