**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"

Apart from the stuff given in "Distance Between Two Points", if you need any other stuff in math, please use our google custom search here.

- 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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