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Distance between Two Points

 

Whenever we need to walk from one place to another, we need to cover the distance between those places. This means the distance is the length between those two places.

In mathematics, distance is defined as the length between two points on the line segment. Thus, we can calculate the distance between points in both 2D and 3D. We can also find the distance in coordinate geometry if we know the coordinates of points in space.

For example, if your house and your neighbour’s house are 50 steps apart, it means the distance between them is 50 steps.

Distance must have a specific unit of measurement. It is measured in the units of length as the distance is nothing but length between two points.

In physics, distance occurs in both straight and curved lines.

But in mathematics, distance is only considered the length between two points when it follows a straight path. Therefore, the curve line distance is not considered as the distance for mathematical calculations.

Distance formula between two points

In 2D, we can find the distance by using the distance formula if we know the value of the positions of the two points. For example, let the coordinates of the two points be A = (x1, y1) and B = (x2, y2). Then according to the distance formula:

image

We need to put the appropriate units whatever are of A and B. To find the distance between 3D planes, the above formula can be modified as:

image1

where, z1 and z2 are the coordinates of the third point that occur in 3D.

How to find the distance between two points?

We must follow the below steps to find the distance between two points:

image2

Example 1: Find the distance between two points having coordinates (3, 4) and (6, 8).

Solution:

We know, according to the distance formula, the distance between two points AB is given by:

image3

Since the coordinates do not have any unit, we need to put units to represent any of the units that could be used above.

Example 2: Find the distance between a line in a 3D plane, having coordinates (4, 5), (5, 7) and (10, 12).

Solution:

We know, according to the distance formula, the distance between three points is given by:

image4

Since the coordinates do not have any unit, we need to put units to represent any of the units that could be used above.

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