where does the distance formula come from?

Question

* and how is it used?

Answer 1

The distance formula comes from the Pythagorean theorem.

 

Suppose you plot 3 points and when you connect them, they form a triangle.  Lets say your distance between two x-coordinate points is leg A, the distance between two y-coordinate points is leg B, and the distance between the endpoints of leg A and leg B is your hypotenuse D.  Leg A and leg B are perpendicular to each other and their endpoints meet.  Therefore,

 

D² = (x₂ - x₁)² + (y₂ - y₁)²

 

D² = A² + B²

 

 

Square-rooting both sides of equation:

 

D = √(A² + B²)

 

D = √[(x₂ - x₁)² + (y₂ - y₁)²]