4.4. DISTANCE BETWEEN TWO POINTS

To find the distance between two points (x ₁ , y ₁ , z ₁ ) and (x ₂ , y ₂ , z ₂ ).

Let P( x ₁, y ₁, z ₁) and Q( x ₂, y ₂, z ₂) be two given points. Through P and Q, draw PL and QM ?s on the XY-plane meeting it in the points L and M respectively.

Fig. 5

Then in the XY-plane, L is the point ( x ₁, y ₁) and M is ( x ₂, y ₂), so that

Now, through P, draw PR ? QM.

Then clearly

and

In the right-angled triangle PRQ,

?

Cor. The distance of any point ( x, y, z) from the origin