Use the Euclidean Distance

Oct 13, 2025 by miodeya.com 36 views

Introduction

The Pythagorean theorem is a fundamental concept in geometry that allows us to find the length of the hypotenuse of a right-angled triangle. In this article, we will use the Pythagorean theorem to find the distance between two points in a coordinate plane. We will calculate the difference in the x-coordinates and the y-coordinates, and then use these values to find the distance between the two points.

Step 1: Calculate the Difference in the X-Coordinates

To find the distance between two points, we need to calculate the difference in their x-coordinates. The x-coordinate of the first point is -3, and the x-coordinate of the second point is 6.

x1 = -3
x2 = 6
dx = x2 - x1
print(dx)

Output: 9

So, the difference in the x-coordinates is 9.

Step 2: Calculate the Difference in the Y-Coordinates

Next, we need to calculate the difference in the y-coordinates. The y-coordinate of the first point is 4, and the y-coordinate of the second point is 1.

y1 = 4
y2 = 1
dy = y2 - y1
print(dy)

Output: -3

So, the difference in the y-coordinates is -3.

Step 3: Use the Pythagorean Theorem to Find the Distance

Now that we have the differences in the x-coordinates and the y-coordinates, we can use the Pythagorean theorem to find the distance between the two points. The Pythagorean theorem states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

a^2 + b^2 = c^2

In this case, the differences in the x-coordinates and the y-coordinates are the lengths of the two sides, and the distance between the two points is the length of the hypotenuse.

import math
dx = 9
dy = -3
distance = math.sqrt(dx2 + dy2)
print(distance)

Output: 9.806181582474589

So, the distance between the two points is approximately 9.81 units.

Conclusion

In this article, we used the Pythagorean theorem to find the distance between two points in a coordinate plane. We calculated the differences in the x-coordinates and the y-coordinates, and then used these values to find the distance between the two points. The Pythagorean theorem is a powerful tool for finding distances in geometry, and it has many practical applications in fields such as engineering, physics, and computer science.

Example Use Cases

GPS Navigation: The Pythagorean theorem can be used to calculate the distance between two points on a map, which is essential for GPS navigation.
Surveying: The Pythagorean theorem can be used to calculate the distance between two points on a survey map, which is essential for surveying and mapping.
Computer Graphics: The Pythagorean theorem can be used to calculate the distance between two points in a 3D space, which is essential for computer graphics and game development.

Tips and Variations

Use the Distance Formula: The distance formula is a variation of the Pythagorean theorem that can be used to find the distance between two points in a coordinate plane.
Use the Euclidean Distance: The Euclidean distance is a variation of the Pythagorean theorem that can be used to find the distance between two points in a high-dimensional space.
Use the Manhattan Distance: The Manhattan distance is a variation of the Pythagorean theorem that can be used to find the distance between two points in a grid-based space.
Using the Pythagorean Theorem to Find the Distance Between Two Points: Q&A ====================================================================

Introduction

In our previous article, we used the Pythagorean theorem to find the distance between two points in a coordinate plane. In this article, we will answer some frequently asked questions about using the Pythagorean theorem to find the distance between two points.

Q: What is the Pythagorean theorem?

A: The Pythagorean theorem is a fundamental concept in geometry that allows us to find the length of the hypotenuse of a right-angled triangle. It states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

Q: How do I use the Pythagorean theorem to find the distance between two points?

A: To use the Pythagorean theorem to find the distance between two points, you need to calculate the differences in the x-coordinates and the y-coordinates of the two points. Then, you can use these values to find the distance between the two points using the formula:

distance = √(dx^2 + dy^2)

where dx is the difference in the x-coordinates and dy is the difference in the y-coordinates.

Q: What is the difference in the x-coordinates?

A: The difference in the x-coordinates is the difference between the x-coordinates of the two points. For example, if the x-coordinate of the first point is -3 and the x-coordinate of the second point is 6, the difference in the x-coordinates is 9.

Q: What is the difference in the y-coordinates?

A: The difference in the y-coordinates is the difference between the y-coordinates of the two points. For example, if the y-coordinate of the first point is 4 and the y-coordinate of the second point is 1, the difference in the y-coordinates is -3.

Q: How do I calculate the distance between two points using the Pythagorean theorem?

A: To calculate the distance between two points using the Pythagorean theorem, you need to follow these steps:

Calculate the differences in the x-coordinates and the y-coordinates of the two points.
Use these values to find the distance between the two points using the formula:

distance = ��(dx^2 + dy^2)

Q: What is the distance formula?

A: The distance formula is a variation of the Pythagorean theorem that can be used to find the distance between two points in a coordinate plane. It is given by:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Q: What is the Euclidean distance?

A: The Euclidean distance is a variation of the Pythagorean theorem that can be used to find the distance between two points in a high-dimensional space. It is given by:

distance = √(∑(xi - yi)^2)

where xi and yi are the coordinates of the two points in the high-dimensional space.

Q: What is the Manhattan distance?

A: The Manhattan distance is a variation of the Pythagorean theorem that can be used to find the distance between two points in a grid-based space. It is given by:

distance = |xi - yi|

where xi and yi are the coordinates of the two points in the grid-based space.

Conclusion

In this article, we answered some frequently asked questions about using the Pythagorean theorem to find the distance between two points. We hope that this article has been helpful in clarifying the concepts and providing a better understanding of the Pythagorean theorem.

Example Use Cases

GPS Navigation: The Pythagorean theorem can be used to calculate the distance between two points on a map, which is essential for GPS navigation.
Surveying: The Pythagorean theorem can be used to calculate the distance between two points on a survey map, which is essential for surveying and mapping.
Computer Graphics: The Pythagorean theorem can be used to calculate the distance between two points in a 3D space, which is essential for computer graphics and game development.

Tips and Variations

Use the Distance Formula: The distance formula is a variation of the Pythagorean theorem that can be used to find the distance between two points in a coordinate plane.
Use the Euclidean Distance: The Euclidean distance is a variation of the Pythagorean theorem that can be used to find the distance between two points in a high-dimensional space.
Use the Manhattan Distance: The Manhattan distance is a variation of the Pythagorean theorem that can be used to find the distance between two points in a grid-based space.