DISTANCE BETWEEN TWO POINTS

Distance Between Two Points :

Here we are going to see, how to find the distance between two points. 

Distance Between Two Points (x ₁, y₁) and (x₂ , y₂)

√(x₂-x₁)²+(y₂-y₁)²

Example 1 :

Find the distance between the points A (-12,3) and B(2,5)

Solution:

Distance between the points A and B

√(x₂-x₁)²+(y₂-y₁)²

Here x₁ = -12  y₁ = 3 x₂ = 2  and  y₂ = 5

=  √[(2-(-12)]² + (5-3)²

=   √(2+12)² + (2)²

=  √(14)² + 4

=   √200

=   √2 x 10 x 10

=   10 √2

Example 2 :

Find the distance between the points P (-2,-3) and Q(6,-5)

Solution:

Distance between the points P and Q

√(x₂-x₁)²+(y₂-y₁)²

Here x₁ = -2, y₁ = -3, x₂ = 6  and  y₂ = -5

=  √(6-(-2)² + [(-5-(-3)]²

=  √(6+2)² + (-5+3)²

=   √(8)² + (-2)²

=  √64 + 4

=   √68

=  √2 x 2 x 17

=  2 √17

Example 3 :

Find the distance between R (-7,2) and S(3,2)

Solution:

Here x₁ = -7, y₁ = 2, x₂ = 3  and  y₂ = 2

=  √[(3-(-7)]² + [(-2-(2)]²

=  √(3+7)² + (-2-2)²

=  √(10)² + (-4)²

=  √100 + 16

=  √116

=  √2 x 2 x 2 x 2 x 7

=  2 x 2 √7

=   4 √7

Using distance formula we can show whether

(i) Three given points are collinear or from right triangle, isosceles triangle or equilateral triangle

(ii) Four given points from a parallelogram, rectangle, square or rhombus.

After having gone through the stuff given above, we hope that the students would have understood, "Distance Between Two Points"

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Related topics

• Finding distance between two points worksheet
• Distance between two points word problems
• Using Pythagorean theorem to find distance between two points
• How to determine if points are collinear using distance formula
• Conditions for collinear points
• Naming collinear and coplanar points
• How to Check if Given Four Points Form a Square 
• How to Check if Given Four Points Form a Rectangle
  
• How to Check If the Given Points Form a Parallelogram
  
• How to Check if the Given Four Points Form a Rhombus
  
• Show That the Points are the Vertices of a Right Triangle
  

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