Distance Between 3 Points Calculator

Formula

The formula for calculating the average distance between three points is:

\[ D = \frac{D1 + D2 + D3}{3} \]

where:

• \(D1\) is the distance between points 1 and 2,
• \(D2\) is the distance between points 1 and 3,
• \(D3\) is the distance between points 2 and 3.

These distances are calculated using the Euclidean distance formula:

\[ D1 = \sqrt{(X2 - X1)^2 + (Y2 - Y1)^2} \] \[ D2 = \sqrt{(X3 - X1)^2 + (Y3 - Y1)^2} \] \[ D3 = \sqrt{(X3 - X2)^2 + (Y3 - Y2)^2} \]

Example Calculation

Consider the following points:

• Point 1: \( (1, 2) \)
• Point 2: \( (3, 5) \)
• Point 3: \( (6, 8) \)

Step 1: Calculate \( D1 \).

\[ D1 = \sqrt{(3 - 1)^2 + (5 - 2)^2} = \sqrt{4 + 9} = 3.6055512755 \]

Step 2: Calculate \( D2 \).

\[ D2 = \sqrt{(6 - 1)^2 + (8 - 2)^2} = \sqrt{25 + 36} = 7.8102496759 \]

Step 3: Calculate \( D3 \).

\[ D3 = \sqrt{(6 - 3)^2 + (8 - 5)^2} = \sqrt{9 + 9} = 4.2426406871 \]

Step 4: Calculate the average distance.

\[ D = \frac{3.6055512755 + 7.8102496759 + 4.2426406871}{3} = 5.2194805462 \]

Common FAQs

1. What is the distance between three points?

   • The distance between three points is the average distance between all combinations of the three given points.

2. Is the average distance formula limited to only three points?

   • The specific formula is designed for three points, but similar logic can be extended to find the average distance among any number of points.

3. How is this different from finding the centroid or geometric center?

   • The centroid is the point representing the average position of all the given points, while this calculation determines the average distance between every pair of the three points directly.