Who Developed the Distance Formula?

We all have studied about polynomials in our school. Can you recall it? Let’s discuss the history of the distance formula and its origin. Aside from being educated in Greece, the inventor of the distance formula traveled the world to learn from other civilizations. Pythagoras was his name. You may recognize the name because he was also the creator of the Pythagorean theorem. Earlier versions of the Distance Formula date back to around 600 BC.

You want to travel to Bangkok from Mumbai for a concert by your favourite artist, but you don’t know how far it is. These cities are nothing more than two points on a map with specific latitudes and longitudes. So, how do you determine the distance between two points? That’s simple. You make use of the distance formula. This is how we do it. In this article, we are going to discuss the distance formula and its applications.

How to Calculate the Distance Between Two Points using the Distance Formula?

Now, let’s know what the distance formula is! The distance formula, which is derived from the Pythagorean Theorem, is generally used to calculate the distance between two points in the plane. The length of the line connecting two points is known to be the distance between them. If the two points are on the same horizontal or vertical line, the distance can be calculated by subtracting the non-identical coordinates.


Distance formulas are used in analytic geometry to calculate the distance 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 other things. For example, we can use the distance formula to find the lengths of a triangle’s sides and determine whether the triangle is scalene, isosceles, or equilateral.

Applications of Distance Formula

The distance formula is useful in many other areas of mathematics as well as in many real-life situations. The distance formula can be used for a variety of purposes, some of which are listed below.


  1. It is employed in navigation. The distance formula is used by the pilot of a plane to calculate the distance between their plane and the other plane. They determine the plane’s coordinates and then use the distance formula to calculate the distance.


  1. Let’s look at another example. If we want to find the length of a building with given coordinates for the foot and top, we can use the distance formula. The distance formula is also used by the ship for navigation.


  1. The distance formula can be used to calculate the distance of any point from the origin.


  1. The complex number is represented in the arg-and plane, and the formula for calculating its magnitude is derived from the distance formula.


  1. The distance formula can be used to calculate the distance between two points in three-dimensional and n-dimensional planes.


  1. The distance formula can be used to derive the magnitude formula, which can be used to calculate the magnitude of a vector.

Important Points to Keep in Mind About Distance Formula!


The following are the key points concerning the distance formula.


  • The distance calculated by the distance formula is always positive. This is because the x and y coordinates are squared before being added together, the formula will always result in a positive number. A negative number squared is equivalent to multiplying the negative by itself, yielding a positive number.
  • The calculated distance is the shortest linear distance between the two points.
  • The distance formula yields the same result for points in any of the four quadrants.


To learn more about these concepts in a fun and easy way, visit Cuemath.

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