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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