Distance between Two Points

Let us learn about Distance between Two Points in three-dimensional system.

Let P(x1, y1, z1) and Q ( x2, y2, z2)
be two points referred to a system of
rectangular axes OX, OY and OZ.
Through the points P and Q draw planes
parallel to the coordinate planes so as to
form a rectangular parallelopiped with one
diagonal PQ.
Now, since ∠PAQ is a right
angle, it follows that, in triangle PAQ,
PQ2 = PA2 + AQ2 ... (1)
Also, triangle ANQ is right angled triangle with ∠ANQ a right angle.
Therefore AQ2 = AN2 + NQ2
... (2)
From (1) and (2), we have
PQ2 = PA2 + AN2 + NQ2
Now PA = y2 – y1, AN = x2 – x1 and NQ = z2 – z1
Hence PQ2 = (x2 – x1)2 + (y2 – y1)2 + (z2 – z1)2

Therefore PQ = This gives us the distance between two points (x1, y1, z1) and (x2, y2, z2).

In particular, if x1 = y1 = z1 = 0, i.e., point P is origin O, then OQ =


which gives the distance between the origin O and any point Q (x2, y2, z2).
Hope the above explanation helped you, now let me explain you to find Distance in graph.