How to Calculate Distance between Two Points

Distance between two points can be calculated in two ways i.e. using a scale or by using Pythagorean Theorem. The easiest method is by using a scale. This article on how to calculate distance between two points will show you how to use both these methods. These methods use the basics of mathematics.

To calculate the distance between two points using a scale, plot two points on a paper. Join both these lines by a segment. Place a scale on this and measure the distance. This is the distance between the two points. The unit for measuring distance between two points is either cm, m or km.

Calculating distance between two points using Pythagoras theorem:

If you are familiar with the Pythagoras theorem, which you must have learnt in your school, then it is not at all difficult for you to learn how to calculate the distance between two points.

This theorem is used in a right angled triangle to measure the length of unknown side and it is given as,

AB2 = AC2 + BC2

In the above formula,

  • AB is the length of the hypotenuse of the triangle
  • AC and BC are the other two sides of the triangle

You will have to use this formula for the points plotted on a graph paper or if the points are not plotted on a graph paper then draw the Cartesian system about the points.

The formula for calculating distance between two points plotted on a Cartesian system is given as,

d = √(x2 – x1)2 + (y2 – y1)2

Where, (x1, y1) and (x2, y2) are two points.

Steps for calculating distance between two points:

Suppose you have been given two points (–2, 1) and (1, 5), and you want to find out the distance between these points.

Here,

  • (x1, y1) corresponds to (–2, 1)
  • (x2,y2) corresponds to (1, 5)
  • Step 1: Plot the points on the graph paper and draw a line to join these points.
  • Step 2: Using these points as two of the vertices of the triangle, draw a right angled triangle drawing two lines from these vertices that come in contact at a single point.
  • Step 3: Note down the x and y coordinates of this new vertex or point. This will help you in finding the lengths of horizontal and vertical sides.
  • Step 4: You can now find out the lengths by subtracting the x values and y values of the lines and find out the length of the third side using Pythagoras theorem or you can simply place the above values of x1, x2, y1 and y2.

Therefore,

d = √(x2 – x1)2 + (y2 – y1)2

d = √ (5-1)2 + (1-(-2))2

d = √ (4)2 + (3)2

d = √16 +9

d = √25

d = 5

Hence, the distance between two points is 5.

Placing the values of both the coordinates in the calculators which are available online, you can calculate the distance between two points with much less effort.


Related Content:

  1. How to Calculate Perimeter of a Triangle
  2. How to Calculate Area of Hexagon
  3. How to Calculate Area of a Triangle
  4. How to Calculate Centroid
  5. How to Calculate Perimeter of a Rectangle

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