Exercise 12.3
1. Find the coordinates of the point which divides the line segment joining the points 
and 
in the ratio:
(i) 2: 3 internally,
(ii) 2: 3 externally.
Ans. (i) Let P
be any point which divides the line segment joining points A
and B in the ratio 2: 3 internally. Then
Therefore, Coordinates of P are 
(ii) Let P be any point which divides the line segment joining points A and B in the ratio 2: 3 externally. Then
Therefore, Coordinates of P are 
2. Given that P
Q
and R
are collinear. Find the ratio in which Q divides PR.
Ans. Let Q divides the line segment joining points P
and R in the ratio 
internally. Then
Coordinates of Q are 
According to question, 
Therefore, Q divides the line segment joining the points P and R in the ratio 1: 2.
3. Find the ratio in which the YZ-plane divides the line segment formed by joining the points 
and 
Ans. Let the line segment joining points A and B
be divided by YZ-plane at a point C in the ratio internally. Then
Coordinates of C are 
According to question, C lies on YZ-plane, i.e., 
Therefore, the required ratio is 2: 3.
4. Using section formula, show that the points A
B
and C
are collinear.
Ans. Let the points B divides the line segment joining A
and C in the ratio internally.
Then coordinates of B = 
Now 
5. Find the coordinates of the points which trisect the line segment joining the points P
and Q
Ans. Let R and S be two points which trisect the line segment PQ.
Then PR = RS = SQ
Point R divides the lines segment PQ in the ratio 1: 2.
Then Coordinates of R = 
= 
Again, Point S divides the line segment PQ in the ratio 2: 1.
Then Coordinates of S = 
= 