Find The Distance Between The Points { (12.7, -10.9)$}$ And { (12.7, -19)$}$.

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Introduction

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In mathematics, the distance between two points in a 2D plane is a fundamental concept that has numerous applications in various fields, including physics, engineering, and computer science. The distance between two points can be calculated using the Euclidean distance formula, which is a straightforward and efficient method for determining the distance between two points in a 2D plane.

What is Euclidean Distance?

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The Euclidean distance, also known as the straight-line distance, is the shortest distance between two points in a 2D plane. It is calculated using the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.

Euclidean Distance Formula

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The Euclidean distance formula is given by:

$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$

where $d$ is the distance between the two points, $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points, and $x_1$, $y_1$, $x_2$, and $y_2$ are the individual coordinates of the two points.

Calculating the Distance Between Two Points

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To calculate the distance between two points, we need to substitute the coordinates of the two points into the Euclidean distance formula. Let's consider the two points $(12.7, -10.9)$ and $(12.7, -19)$.

Step 1: Identify the Coordinates of the Two Points

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The coordinates of the two points are:

• $(x_1, y_1) = (12.7, -10.9)$
• $(x_2, y_2) = (12.7, -19)$

Step 2: Substitute the Coordinates into the Euclidean Distance Formula

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Substituting the coordinates of the two points into the Euclidean distance formula, we get:

$$d = \sqrt{(12.7 - 12.7)^2 + (-19 - (-10.9))^2}$$

Step 3: Simplify the Expression

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Simplifying the expression, we get:

$$d = \sqrt{(0)^2 + (-8.1)^2}$$

$$d = \sqrt{0 + 65.61}$$

$$d = \sqrt{65.61}$$

Step 4: Calculate the Square Root

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Calculating the square root, we get:

$$d = 8.1$$

Conclusion

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In this article, we have discussed the concept of Euclidean distance and how to calculate it using the Euclidean distance formula. We have also applied the formula to calculate the distance between two points in a 2D plane. The distance between the points $(12.7, -10.9)$ and $(12.7, -19)$ is $8.1$ units.

Frequently Asked Questions

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Q: What is the Euclidean distance formula?

A: The Euclidean distance formula is given by $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

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

A: To calculate the distance between two points, substitute the coordinates of the two points into the Euclidean distance formula and simplify the expression.

Q: What is the distance between the points $(12.7, -10.9)$ and $(12.7, -19)$?

A: The distance between the points $(12.7, -10.9)$ and $(12.7, -19)$ is $8.1$ units.

References

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• [1] Wikipedia. (2023). Euclidean distance. Retrieved from https://en.wikipedia.org/wiki/Euclidean_distance
• [2] Khan Academy. (2023). Distance formula. Retrieved from https://www.khanacademy.org/math/geometry/geometry-distance-formula/geometry-distance-formula/v/geometry-distance-formula

Code

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Here is a Python code snippet that calculates the distance between two points using the Euclidean distance formula:

import math
def calculate_distance(x1, y1, x2, y2):
"""
Calculate the distance between two points using the Euclidean distance formula.
Args:
    x1 (float): The x-coordinate of the first point.
    y1 (float): The y-coordinate of the first point.
    x2 (float): The x-coordinate of the second point.
    y2 (float): The y-coordinate of the second point.

Returns:
    float: The distance between the two points.
"""
return math.sqrt((x2 - x1)**2 + (y2 - y1)**2)

x1, y1 = 12.7, -10.9
x2, y2 = 12.7, -19
distance = calculate_distance(x1, y1, x2, y2)
print("The distance between the points is:", distance)

This code defines a function calculate_distance that takes the coordinates of two points as input and returns the distance between them using the Euclidean distance formula. The example usage demonstrates how to use the function to calculate the distance between the points $(12.7, -10.9)$ and $(12.7, -19)$.

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Introduction

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In our previous article, we discussed the concept of Euclidean distance and how to calculate it using the Euclidean distance formula. In this article, we will answer some frequently asked questions about Euclidean distance to help you better understand this concept.

Q&A

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Q: What is the Euclidean distance formula?

A: The Euclidean distance formula is given by $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$, where $d$ is the distance between the two points, $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points.

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

A: To calculate the distance between two points, substitute the coordinates of the two points into the Euclidean distance formula and simplify the expression.

Q: What is the distance between the points $(12.7, -10.9)$ and $(12.7, -19)$?

A: The distance between the points $(12.7, -10.9)$ and $(12.7, -19)$ is $8.1$ units.

Q: What is the difference between Euclidean distance and Manhattan distance?

A: Euclidean distance is the shortest distance between two points in a 2D plane, while Manhattan distance is the sum of the absolute differences of the coordinates of the two points.

Q: Can I use the Euclidean distance formula to calculate the distance between three points?

A: No, the Euclidean distance formula is used to calculate the distance between two points. To calculate the distance between three points, you need to use the triangle inequality theorem.

Q: How do I calculate the distance between two points in a 3D space?

A: To calculate the distance between two points in a 3D space, use the Euclidean distance formula in three dimensions: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}$.

Q: What is the significance of Euclidean distance in real-world applications?

A: Euclidean distance has numerous applications in real-world scenarios, such as calculating the distance between two cities, determining the proximity of two objects, and measuring the similarity between two data points.

Q: Can I use the Euclidean distance formula to calculate the distance between two points in a non-Euclidean space?

A: No, the Euclidean distance formula is only applicable in Euclidean spaces. In non-Euclidean spaces, such as spherical or hyperbolic spaces, you need to use different distance metrics.

Conclusion

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In this article, we have answered some frequently asked questions about Euclidean distance to help you better understand this concept. We hope that this article has provided you with a deeper understanding of Euclidean distance and its applications.

Frequently Asked Questions (FAQs)

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Q: What is the Euclidean distance formula?

A: The Euclidean distance formula is given by $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

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

A: To calculate the distance between two points, substitute the coordinates of the two points into the Euclidean distance formula and simplify the expression.

Q: What is the distance between the points $(12.7, -10.9)$ and $(12.7, -19)$?

A: The distance between the points $(12.7, -10.9)$ and $(12.7, -19)$ is $8.1$ units.

References

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• [1] Wikipedia. (2023). Euclidean distance. Retrieved from https://en.wikipedia.org/wiki/Euclidean_distance
• [2] Khan Academy. (2023). Distance formula. Retrieved from https://www.khanacademy.org/math/geometry/geometry-distance-formula/geometry-distance-formula/v/geometry-distance-formula

Code

---

Here is a Python code snippet that calculates the distance between two points using the Euclidean distance formula:

import math
def calculate_distance(x1, y1, x2, y2):
"""
Calculate the distance between two points using the Euclidean distance formula.
Args:
    x1 (float): The x-coordinate of the first point.
    y1 (float): The y-coordinate of the first point.
    x2 (float): The x-coordinate of the second point.
    y2 (float): The y-coordinate of the second point.

Returns:
    float: The distance between the two points.
"""
return math.sqrt((x2 - x1)**2 + (y2 - y1)**2)


x1, y1 = 12.7, -10.9
x2, y2 = 12.7, -19
distance = calculate_distance(x1, y1, x2, y2)
print("The distance between the points is:", distance)

This code defines a function calculate_distance that takes the coordinates of two points as input and returns the distance between them using the Euclidean distance formula. The example usage demonstrates how to use the function to calculate the distance between the points $(12.7, -10.9)$ and $(12.7, -19)$.