1. What is Manhattan Distance?

The Manhattan Distance (also called Taxicab Distance or L1 Distance) is a measure of the distance between two points in a grid-based system where movement is restricted to horizontal and vertical paths only, like navigating the streets of Manhattan.

2. How Does the Calculator Work?

The calculator uses the Manhattan Distance formula:

Where:

• \( (x_1, y_1) \) — Coordinates of the first point
• \( (x_2, y_2) \) — Coordinates of the second point
• \( | \cdot | \) — Absolute value function

Explanation: The formula calculates the sum of the absolute differences of their Cartesian coordinates.

3. Applications of Manhattan Distance

Details: Commonly used in computer science (pathfinding algorithms), image processing, urban planning, and any scenario where movement is constrained to grid-like paths.

4. Using the Calculator

Tips: Enter the coordinates of two points in 2D space. The calculator will compute the Manhattan Distance between them.

5. Frequently Asked Questions (FAQ)

Q1: How is Manhattan Distance different from Euclidean Distance?
A: Manhattan Distance sums absolute differences (grid path), while Euclidean Distance measures straight-line distance between points.

Q2: Can Manhattan Distance be negative?
A: No, because it uses absolute values of the differences.

Q3: Does the order of points matter in calculation?
A: No, MD(A,B) = MD(B,A) because of the absolute value function.

Q4: Can this be extended to higher dimensions?
A: Yes, for n-dimensional points: MD = Σ|a_i - b_i| for i=1 to n.

Q5: Why is it called "Manhattan" Distance?
A: It resembles the path a taxicab would take in Manhattan's grid-like street system.