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**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 = =

Q4 of ex 12.3 is not solved tatally. It’s solution is half way done.

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