Ramu also writes the distance formulas as AB = √((x − x )² + ( y − y )²). Why?
Answers
Given : distance formulas as AB = √ (x₂ - x₁)² + (y₂ - y₁)²
To find : Why
Solution:
Let say point A = ( x₁ , y₁)
Point B = (x₂ , y₂)
AB = √ (x₂ - x₁)² + (y₂ - y₁)²
Lets draw a Ray AX parallel to x axis
Hence any point on AX would be (x , y₁)
Now Draw a perpendicular from B at AX meeting at C
AX is parallel to x axis hence BC would be parallel to y axis
any point on BC would be (x₂ , y )
Intersection point C would be
( x₂ , y₁)
Length of AC = x₂ - x₁
Length of BC = y₂ - y₁
Applying Pythagoras theorem in right angle triangle ACB
AB² = AC² + CB²
=> AB² = (x₂ - x₁)² + (y₂ - y₁)²
AB = √ (x₂ - x₁)² + (y₂ - y₁)²
Same as distance formula
Learn More :
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hope this helps you.
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