# Distance Between Two Points The length of the line segment connecting two points is called the distance between them. The length of the line segment connecting the specified coordinates can be used to compute the distance between two points in coordinate geometry. The length of the line segment connecting two points is defined as the distance between them. The length of the line segment connecting the given coordinates can be used to calculate the distance between two points in coordinate geometry. Let’s look at the formula for calculating the distance between two points in a two-dimensional or three-dimensional plane.

Let us find out how to calculate the distance between two points in a 2D and 3D plane using the formula.

## What is the Distance Formula?

Do you know what distance is? Distance is a mathematical quantity used to determine how far two points are from each other in a two-dimensional space. This parameter is one of the most crucial mathematical quantities. It is used to model quantities such as the velocity of a moving body, the magnitude, and direction of electrical and gravitational forces, and signal processing in advanced mathematics and physics.

The distance formula can be used to compute the distance between two places given their coordinates. We can use the Euclidean distance formula to calculate the distance between any two points in the 2-D plane.

To understand the topic in a better way, you can visit the Cuemath website.

## Distance Between Two Points

The length of the line segment connecting two places is the distance between them. There’s just one line that connects the two places. So, finding the length of the line segment linking two places can be used to compute the distance between them. For instance, if A and B are two points and AB = 20 cm, it signifies that the distance between them is 20 cm.

[Note – The length of the line segment connecting two points is the distance between them (but this line segment cannot be a curve joining them). It’s important to keep in mind that the distance between two points is usually positive.]

### Formula for Distance Between Two Points

The formula for calculating the distance, d, between two points with coordinates of ( a1, b1 ) and ( a2, b2 ) is as follows:

d =√ [ (a2 – a1 )2 + ( b2 – b1 )2 ] ( pronounced as square root of a2 minus a1 whole square plus b2 minus b1 whole square )

This is known as the Distance Formula.

The 3-D distance formula, expressed as, can be used to calculate the distance between two points in a 3-D plane.

d =√ [ (a2 – a1 )2 + ( b2 – b1 )2 + ( c2 – c1 )2] ( pronounced as square root of a2 minus a1 whole square plus b2 minus b1 whole square plus c2 minus c1 whole square )

## Is it Possible for the Distance Between Two Points to be Negative?

No, a distance between two points cannot be negative. This can be thought of in three ways:

Distance is a physical quantity that expresses how far two points are from each other, and it cannot be negative. The square root of the sum of two positive numbers equals distance. The sum of two positive numbers is always positive, as is the square root of a positive number.

Even if the distance between two points is zero, it is still a non-negative value, so the distance cannot be negative.

## Applications of Distance Formula

• To prove that a given figure is a square, show that the four sides and diagonals are equal.

• Prove that the four sides of a given figure are equal to prove that it is a rhombus.

• To prove that a given figure is a rectangle, show that the opposite sides are equal, as well as the diagonals.

• Prove that the opposite sides of a given figure are equal to prove that it is a parallelogram.

• To demonstrate that a given figure is a parallelogram rather than a rectangle, show that its opposite sides are equal but the diagonals are not.

• To demonstrate that a given figure is a rhombus rather than a square, show that all of its sides are equal but the diagonals are not. 