What is Euclidean Distance?

The measure which gives the distance between any two points in an n-dimensional plane is known as Euclidean Distance. Euclidean distance between two points in the Euclidean space is defined as the length of the line segment between two points.

Euclidean distance is like measuring the straightest and shortest path between two points. Imagine you have a string and you stretch it tight between two points on a map; the length of that string is the Euclidean distance. It tells you how far apart the two points are without any turns or bends, just like a bird would fly directly from one spot to another.

Euclidean Distance

Euclidean Distance is defined as the distance between two points in Euclidean space. To find the distance between two points, the length of the line segment that connects the two points should be measured.

In this article, we will explore what is Euclidean distance, the Euclidean distance formula, its Euclidean distance formula derivation, Euclidean distance examples, etc.

Euclidean Distance

Table of Content

  • What is Euclidean Distance?
  • Euclidean Distance Formula
    • Euclidean Distance in 3D
    • Euclidean Distance in nD
  • Euclidean Distance Formula Derivation
  • Euclidean Distance and Manhattan Distance
  • Solved Questions on Euclidean Distance
  • Practice Problems on Euclidean Distance

Similar Reads

What is Euclidean Distance?

The measure which gives the distance between any two points in an n-dimensional plane is known as Euclidean Distance. Euclidean distance between two points in the Euclidean space is defined as the length of the line segment between two points....

Euclidean Distance Formula

Consider two points (x1, y1) and (x2, y2) in a 2-dimensional space; the Euclidean Distance between them is given by using the formula:...

Euclidean Distance Formula Derivation

Euclidean Distance Formula is derived by following the steps added below:...

Euclidean Distance and Manhattan Distance

Differences between the Euclidean and Manhattan methods of measuring distance are listed in the following table:...

Conclusion

Euclidean Distance is a metric for measuring the distance between two points in Euclidean space, reflecting the length of the shortest path connecting them, which is a straight line. The formula for calculating Euclidean Distance depends on the dimensionality of the space. In a 2-dimensional plane, the distance d between points is, d = d = √[(x2 – x1)2 + (y2 – y1)2]. In 3D, d = √[(x2 – x1)2 + (y2 – y1)2+ (z2 – z1)2]....

Solved Questions on Euclidean Distance

Here are some sample problems based on the distance formula....

Practice Problems on Euclidean Distance

P1: Calculate the Euclidean distance between points P(1, 8, 3) and Q(6, 6, 8)....

Euclidean Distance – FAQs

Define Euclidean Distance....