Distance Formula

Examples, videos, worksheets, and solutions to help Grade 8 students learn the distance formula that uses the Pythagorean Theorem.

What is the Distance Formula?
The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:

\(D = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} \)

The following diagram shows the distance formula and how it can be derived from the Pythagorean Theorem. Scroll down the page for more examples and solutions.

 

Geometry Worksheets
Practice your skills with the following geometry worksheets:
Printable & Online Geometry Worksheets

Coordinate Geometry Worksheets
Practice your skills with the following coordinate geometry worksheets:
Printable & Online Coordinate Geometry Worksheets

Deriving the Distance Formula from the Pythagorean Theorem
Visualize the two points on a coordinate plane and construct a right triangle between them.

1. Plot the two points: Let’s say you have point A(x₁, y₁) and point B(x₂, y₂)
   
2. Visualize Points as a Right Triangle:
   The horizontal leg = |x₂ - x₁| (difference in x-coordinates).
   The vertical leg = |y₂ - y₁| (difference in y-coordinates).
   The distance d is the hypotenuse.
   
3. Using the Pythagorean Theorem:
   \(d^2 = (x_2 - x_1)^2 + (y_2 - y_1)^2 \)
   \(d = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} \)

How the distance formula comes from the Pythagorean Theorem?
Example of finding the distance between two points.

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Distance Formula Between Two Points

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How to find the distance on a line using the distance formula?

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Brief explanation of distance formula and an example

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