Distance Formula in a 2D Plane

Assume there are two points, A and B, in a coordinate plane, the first quadrant. (a, b) are the coordinates of point A, and (a, b) are the coordinates of point B. (p, q). The distance between points A and B abbreviated AB, must be calculated as follows:

[Tex]\bold{\text{AB} = \sqrt{{(a-p)}^2+{(b-q)}^2}} [/Tex]

How to Find Distance Between Two Points?

To find the distance between two points, we can use the following steps:

1. Identify the coordinates of the two points.
2. Use the formula discussed above to calculate distance between two point in two dimensional plane.

Let’s discuss an example for the same.

Example: Find the distance between two points X(5, 10) and Y(2, 4).

Solution:

As given points are X(5, 10) and Y(2, 4).

So, the distance between them is using the formula is

D = [Tex]\sqrt{{(5-2)}^2+{(10-4)}^2} [/Tex]

⇒ D = [Tex]\sqrt{{(3)}^2+{(6)}^2} [/Tex]

⇒ D = [Tex]\sqrt{9+36} [/Tex]

⇒ D = [Tex]\sqrt{9+36} [/Tex]

⇒ D = [Tex]\sqrt{45} = 3\sqrt{5} [/Tex]

So, the distance between X and Y is 3√5 units.

Derivation for Distance Formula

Let us assume that two points are present on a 2-dimensional plane that is A and B with coordinates (a, b) and (p, q). Now we construct a right angle triangle i.e.AJB in which AB is a hypotenuse. Now we find the distance between points A and B.

By Pythagoras Theorem,

AB² = AJ² + BJ²

⇒ AB² = (a – p)² + (b – q)²

⇒ AB = √{(a – p)² + (b – q)²}

Let’s consider an example to learn how to use the formula.

Distance Between Two Points is the length of line segment that connect any two points in coordinate plane in coordinate geometry. It can be calculated using distance formula for 2D or 3D. It represents the shortest path between two locations in a given space.

In this article, we will learn how to find the distance between two points. Let’s first understand what are point before learning the methods and formula to find the distance between them.