Python Program to Find Distance Between Two Points

You can find the distance between two points (x1, y1) and (x2, y2) in Python using the formula distance = ((x2 - x1)**2 + (y2 - y1)**2)**0.5.

Examples

Input(0, 0) and (3, 4)

Output5.0

Input(1, 2) and (4, 6)

Output5.0

Input(2, 3) and (2, 3)

Output0.0

How to Think About It

To find the distance between two points, think of the points as corners of a right triangle. The distance is the length of the hypotenuse. Use the difference in x-coordinates and y-coordinates, square them, add them, and then take the square root.

Algorithm

1

Get the coordinates of the first point (x1, y1).

2

Get the coordinates of the second point (x2, y2).

3

Calculate the difference in x-coordinates: dx = x2 - x1.

4

Calculate the difference in y-coordinates: dy = y2 - y1.

5

Calculate the distance using the formula: distance = square root of (dx squared + dy squared).

6

Return or print the distance.

Code

python

def distance_between_points(x1, y1, x2, y2):
    distance = ((x2 - x1)**2 + (y2 - y1)**2)**0.5
    return distance

# Example usage
print(distance_between_points(0, 0, 3, 4))

Output

5.0

Dry Run

Let's trace the example (0, 0) and (3, 4) through the code

1

Input points

x1 = 0, y1 = 0, x2 = 3, y2 = 4

2

Calculate differences

dx = 3 - 0 = 3, dy = 4 - 0 = 4

3

Calculate distance

distance = sqrt(3**2 + 4**2) = sqrt(9 + 16) = sqrt(25) = 5.0

4

Return result

distance = 5.0

Step	dx	dy	distance
Calculate differences	3	4
Calculate distance			5.0

Why This Works

Step 1: Calculate differences

Subtract the x and y coordinates to find the horizontal and vertical distances between points using dx = x2 - x1 and dy = y2 - y1.

Step 2: Apply Pythagorean theorem

Square the differences and add them: dx**2 + dy**2 gives the square of the distance.

Step 3: Find the distance

Take the square root of the sum using **0.5 to get the actual distance between the points.

Alternative Approaches

Using math.sqrt function

python

import math

def distance_between_points(x1, y1, x2, y2):
    return math.sqrt((x2 - x1)**2 + (y2 - y1)**2)

print(distance_between_points(0, 0, 3, 4))

This uses the built-in math.sqrt for clarity and readability; it is slightly more explicit.

Using numpy library

python

import numpy as np

def distance_between_points(p1, p2):
    return np.linalg.norm(np.array(p2) - np.array(p1))

print(distance_between_points((0, 0), (3, 4)))

This method is useful when working with arrays or many points but requires installing numpy.

Complexity: O(1) time, O(1) space

Time Complexity

The calculation involves a fixed number of arithmetic operations, so it runs in constant time.

Space Complexity

Only a few variables are used to store intermediate results, so space usage is constant.

Which Approach is Fastest?

Using **0.5 or math.sqrt() both run in constant time; numpy adds overhead but is better for many points.

Approach	Time	Space	Best For
Using **0.5	O(1)	O(1)	Simple scripts without imports
Using math.sqrt	O(1)	O(1)	Clearer code with standard library
Using numpy.linalg.norm	O(1)	O(1)	Working with arrays or many points