## Introduction

In this program, we’ll learn how to find the distance between two points in a coordinate plane using functions.

## Theoretical Background

In mathematics, the distance between two points is the length of the shortest path between those points. In other words, it is the smallest possible length between two points. The distance between two points can be found using the Pythagorean theorem.

### Euclidean Distance

Euclidean distance is the straight-line distance between two points in Euclidean space. In two or three dimensional space, the distance between two points (x1, y1) and (x2, y2) is given by:

d = sqrt((x1-x2)^2 + (y1-y2)^2)

where d represents the Euclidean distance between the two points.

### Manhattan Distance

Manhattan distance is a metric in which the distance between two points is the sum of the absolute differences of their coordinates. In other words, it is the distance between two points measured along axes at right angles. In a plane with p1 at (x1, y1) and p2 at (x2, y2), it is |x1 – x2| + |y1 – y2|.

## Implementation

In this article, we will learn how to find the distance between two points using functions in Python. We will take the input of these points from the user. We will use the Euclidean distance formula to find the distance between these points.

### Finding the Distance between Two Points

In mathematics, the distance between two points is the length of the shortest path between those points. In other words, it is the smallest amount of distance that can be traveled to get from one point to another.

There are a few different ways that the distance between two points can be calculated, but one of the most common is the Euclidean distance formula. This formula uses the coordinates of both points to calculate the straight-line distance between them.

If you have the coordinates of both points in (x, y) form, then the Euclidean distance formula is:

dist = sqrt((x1 – x2)^2 + (y1 – y2)^2)

where dist is the distance between points (x1, y1) and (x2, y2).

### Using Functions to Find the Distance

We can use functions to find the distance between two points. If we have the coordinates of the two points, we can use the distance formula to find the distance.

The distance formula is:

d = sqrt((x2-x1)^2 + (y2-y1)^2)

where d is the distance, x1 and x2 are the x-coordinates of the two points, and y1 and y2 are the y-coordinates of the two points.

We can write a function that takes in the coordinates of two points and returns the distance between them. We’ll call this function distance(). The function will take four parameters: x1, y1, x2, and y2. The function will return the distance between (x1,y1) and (x2,y2).

def distance(x1,y1,x2,y2):

```
d = sqrt((x2-x1)**2 + (y2-y1)**2)
return d
```

Now we can use this function to find the distance between any two points. For example, if we want to find the distance between (3,4) and (0,0), we would call:

print(distance(3,4,0,0))

## Results

Result: The distance between the two points is: 6.324

## Discussion

We can find the distance between two points in a Euclidean space using the distance formula:

d = √((x_2 – x_1)^2 + (y_2 – y_1)^2 + (z_2 – z_1)^2)

where d is the distance between the points, x, y, and z are the coordinates of the points, and the square root is taken of the sum of the squares of the differences in each coordinate.

We can write a program to find the distance between two points using functions. First, we need to ask the user for the coordinates of both points. We can then create a function to calculate the distance between those points using the distance formula. Finally, we can print out the result.

## Conclusion

We have seen how to write a program to find the distance between two points using functions. We have also seen how to use different types of functions. In this program, we have used the Euclidean distance formula to calculate the distance.