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Manhattan Distance To Point Calculator

Manhattan Distance Formula:

\[ D = |x_2 - x_1| + |y_2 - y_1| \]

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1. What is Manhattan Distance?

The Manhattan Distance, also known as Taxicab Distance or L1 Distance, is a metric between two points in a grid-based system. It represents the sum of the absolute differences of their Cartesian coordinates.

2. How Does the Calculator Work?

The calculator uses the Manhattan Distance formula:

\[ D = |x_2 - x_1| + |y_2 - y_1| \]

Where:

Explanation: The distance is calculated by summing the absolute differences between the x-coordinates and y-coordinates of the two points.

3. Applications of Manhattan Distance

Details: Manhattan Distance is widely used in pathfinding algorithms, computer vision, data analysis, and any application 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 the absolute differences of coordinates, while Euclidean Distance calculates the straight-line distance using the Pythagorean theorem.

Q2: Why is it called "Manhattan" Distance?
A: It's named after the grid-like street layout of Manhattan, where you can only move along streets (like a taxi cab), not diagonally through buildings.

Q3: Can this calculator handle 3D coordinates?
A: This version only calculates 2D distances. For 3D, the formula would extend to \( |x_2-x_1| + |y_2-y_1| + |z_2-z_1| \).

Q4: What are some practical uses of Manhattan Distance?
A: It's used in chess for distance between squares, in image processing, and in algorithms like A* pathfinding where diagonal movement isn't allowed.

Q5: Does the order of points matter in the calculation?
A: No, the distance is the same whether you calculate from point A to B or point B to A.

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