# Distance Formula

**Basic Distance Formula**:

The basic distance formula states that:

The distance “d” between two points A(x1,y1) and B(x2,y2) can be calculated as:

Using this Distance Formula of coordinate geometry we can establish fundamental trigonometric formulae for general angles in a very elegant way. So we shall now prove or derive this formula:

**Derivation or Proof of Distance Formula**:

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

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

Now ,

And Similarly:

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

So ,

Thus ,

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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