Distance Between Two Points





In this page we are going to see how to find the distance between two points.This is basic concept in geometry.This concept will be useful to 9th grade students.Here you can find formula and example problem with solution.You can also get practice problems for this topic.

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

√(x₂ - x₁) ² + (y₂ - y₁) ²

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.

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)

                       =    √196+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 the points R (-7,2) and S(3,2)

Solution:

Distance between the points R and S = √(x₂ - x₁) ² + (y₂ - y₁) ²

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

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Distance Between Two Points to Analytical Geometry