The distance between two points P(x₁, y₁) and Q(x₂, y₂) is the length of the line segment PQ. In this section, we will develop a formula for the distance between any two points in the coordinate system. Before considering this for arbitrary points, we will do it for particular points in the following example.

Example

Find the distance between O(0, 0) and B(3, 4).

Let us plot O(0, 0), B(4, 3) and form the right angled triangle OAB where A is at (4, 0), as shown in the adjacent figure.

Consequently, OB is the hypotenuse of DOAB while OA and AB are the lengths of the horizontal and vertical sides of the triangle such that OA = 4 and AB = 3.

Hence, by Pythagoras’ theorem,

That is, the distance between (0, 0) and (4, 3) is 5.