Page 2 - LESSON NOTE

Distance between Two Points

The distance between the points P( , , ) and Q( , , ) is given by
1
2
1
1
2
2
2
2
2
PQ =√( − ) + ( − ) + ( − )
2
1
2
1
2
1
Section Formula
The coordinates of the point R which divides the line segment joining two points P( , , ) and
1
1
1
,
,
Q( , , ) internally in the ratio m : n are ( 2 + 1 2 + 1 2 + 1 ).
2
2
2
+
+
+
If the point R divides PQ externally in the ratio m : n, then its coordinates are obtained by replacing n by – n.
,
,
So that coordinates of point R will be ( 2 − 1 2 − 1 2 − 1 )
− − −
EXAMPLES
1. A point is on the x -axis. What are its y-coordinate and z-coordinates?
Ans:- If a point is on the x-axis, then its y-coordinates and z-coordinates are zero.
2. Name the octants in which the following points lie: (1, 2, 3), (4, –2, 3), (4, –2, –5), (4, 2, –5), (– 4, 2, –
5),
(– 4, 2, 5), (–3, –1, 6), (2, – 4, –7).
Ans:- The x-coordinate, y-coordinate, and z-coordinate of point (1, 2, 3) are all positive.

Therefore, this point lies in octant I.

The x-coordinate, y-coordinate, and z-coordinate of point (4, –2, 3) are positive, negative, and

positive respectively. Therefore, this point lies in octant IV.

The x-coordinate, y-coordinate, and z-coordinate of point (4, –2, –5) are positive, negative, and

negative respectively. Therefore, this point lies in octant VIII.