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

**Related Topics**

**Section formula****Area of triangle****Area of triangle worksheets****Area of quadrilateral****Centroid****Centroid of the triangle worksheets****Finding missing vertex using centroid worksheet****Midpoint****Distance between - two points worksheet****Slope of the line****Equation of the line****Equation of line using two points worksheet****Equation of the line using point and slope worksheets****Point of intersection of two lines****Point of intersection Worksheets****concurrency of straight line****Concurrency of straight lines worksheet****Circumcentre of a triangle****Circumcentre of Triangle Worksheet****Orthocentre of a triangle****Orthocentre of Triangle Worksheet****Incentre of a triangle****Locus****Perpendicular distance****Angle between two straight lines****Equation of a circle****With center and radius****With endpoints of a diameter****Equation of a circle passing though three points****Length of the tangent to a circle****Equation of the tangent to a circle****Family of circles****Orthogonal circles****Parabola****Ellipse**

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