Home | Math | 10 Examples of the Distance Formula

# 10 Examples of the Distance Formula

September 20, 2023 written by Rida Mirza

The distance formula is a fundamental mathematical tool used to calculate the distance between two points in a Cartesian coordinate system. It plays a important role in geometry, algebra, and various real-world applications.

In this article, we will explore ten examples of the distance formula in math.

### Examples of the Distance Formula

These are examples of distance formula.

### 1: Understanding the Distance Formula

The distance formula is derived from the Pythagorean theorem, calculates the distance ‘d’ between two points with coordinates (x₁, y₁) and (x₂, y₂) in a two-dimensional plane.

Distance = √((x2 – x1)^2 + (y2 – y1)^2)

### 2: Distance between Two Points in a Plane

In a two-dimensional For example, to find the distance between two cities on a map or the length of a line segment in a coordinate plane.

### 3: Distance between Two Points in 3D Space

The distance formula extends to three dimensions, enabling us to calculate the distance between two points in 3D space, such as (x1, y1, z1) and (x2, y2, z2).

Distance = √((x2 – x1)^2 + (y2 – y1)^2 + (z2 – z1)^2)

### 4: Distance between Coordinates on a Map

When using latitude and longitude coordinates, the distance formula helps calculate the great-circle distance between two locations on Earth’s surface.

### 5: Finding the Length of a Line Segment

The distance formula is applied to calculate the length of a line segment between its endpoints.

### 6: Distance between Cities

In geography, the distance formula is used to find the shortest distance between cities on a map, considering the Earth’s curvature.

### 7: Distance in Analytical Geometry

Analytical geometry often involves finding distances between points in various coordinate systems, and the distance formula simplifies these calculations.

### 8: Distance in Physics

Physics uses the distance formula to calculate the spatial separation between objects in motion, helping analyze their trajectories and velocities.