Question

How do you create a Distance Formula?

Answer 1

Definition of distance formula :

The distance between two points is the length of the line joining the two points. If the two points lie on the same horizontal or same vertical line, the distance can be found by subtracting the coordinates that are not the same.

In analytic geometry, the distance formula is used to find the distance measured between two lines, the sum of the lengths of all the sides of a polygon, the perimeter of polygons on a coordinate plane, the area of polygons, and many more.

For example, we can find the lengths of sides of a triangle using the distance formula and determine whether the triangle is scalene, isosceles, or equilateral.

In Euclidean geometry, the distance formula is used to find the distance between the two points in an $XY$ plane. The coordinates of point $M(x_1,y_1)$ and $N(x_2,y_2)$. Then the formula to find the distance between two points $MN$ is $\sqrt{{\mathbf{(}{\mathbf{x}}_{\mathbf{2}}\mathbf{-}{\mathbf{x}}_{\mathbf{1}}\mathbf{)}}^{\mathbf{2}}\mathbf{-}{\mathbf{(}{\mathbf{y}}_{\mathbf{2}}\mathbf{-}{\mathbf{y}}_{\mathbf{1}}\mathbf{)}}^{\mathbf{2}}}$.