Question

कार्तीय निर्देशांक पद्धति में दो बिंदुओं के बीच की दूरी ज्ञात करने हेतु सूत्र निर्मित कीजिए ?​

Answer 1

Answer:

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Answer 2

Given :  कार्तीय निर्देशांक पद्धति में दो बिंदुओं के बीच की दूरी

To Find :   सूत्र निर्मित कीजिए

Solution :

Let say Two points  are

A  = (x₁ , y₁   )    & B = (x₂ , y₂)

distance between two points in the plane​ A & B = √(  (x₂ - x₁)² +  (y₂ - y₁)² )

proof :

Lets draw a line parallel to x axis  passing though A

so slope of line would be zero

Hence  y - y₁  = 0(x - x₁ )

=> line would be  y =  y₁

now draw a  line parallel to y axis passing through point B

line would be  x  = x₂

intersection of both Lines at C would be ( x₂ , y₁)

now ACB will be a right angle triangle at C  ( as x axis & y axis are perpendicular to each other)

now AC =  (x₂ - x₁)

& BC = (y₂ - y₁)

applying Pythagoras theorem

AB² = AC² + BC²

=> AB² =   (x₂ - x₁)² +  (y₂ - y₁)²

=> AB = √(  (x₂ - x₁)² +  (y₂ - y₁)² )

QED

Hence Proved

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