Question

prove that :

The distance between Two points is given by the distance formula ​

Answer 1

Hey Mate

The Distance Formula. The Distance Formula is a useful tool for finding the distance between two points. The formula itself is actually derived from the Pythagorean Theorem. That's why we can claim that this formula is simply the Pythagorean Theorem in disguise.

1. Distance between two points P(x1,y1) and Q(x2,y2) is given by: d(P, Q) = √ (x2 − x1)2 + (y2 − y1)

2 {Distance formula} 2. Distance of a point P(x, y) from the origin is given by d(0,P) = √ x2 + y2. 3.

Derivation or Proof of Distance Formula:

In the adjoining figure , “d” is the distance between two points P(x1 , y1) and Q(x2 , y2).

basic distance formula

Now let us draw “PL” perpendicular to “OX” and “PR” perpendicular to “QM”.


 

And Similarly
 

And now in the right angle triangle PQR applying Pythagorean  Theorem.

This is the basic distance formula and can be used to calculate to find the distance between two points P , Q if their co-ordinates ( x1 , y1 , x2 , y2) are known.

 




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Answer 2

$\textbf{Answer is in Attachment !}$