## RD Sharma Class 10 Solutions Chapter 9 Constructions Ex 9.1

These Solutions are part of RD Sharma Class 10 Solutions. Here we have given RD Sharma Class 10 Solutions Chapter 9 Constructions Ex 9.1

**Other Exercises**

- RD Sharma Class 10 Solutions Chapter 9 Constructions Ex 9.1
- RD Sharma Class 10 Solutions Chapter 9 Constructions Ex 9.2
- RD Sharma Class 10 Solutions Chapter 9 Constructions Ex 9.3

**Question 1.
**

**Determine a point which divides a line segment of length 12 cm internally in the ratio 2 : 3. Also justify your construction.**

**Solution:**

**Steps of construction :**

(i)Draw a line segment AB = 12 cm.

(i)

**(ii)**Draw a ray AX at A making an acute angle with AB.

**(iii)**From B, draw another ray BY parallel to AX.

**(iv)**Cut off 2 equal parts from AX and 3 equal parts from BY.

**(v)**Join 2 and 3 which intersects AB at P.

P is the required point which divides AB in the ratio of 2 : 3 internally.

**Question 2.
**

**Divide a line segment of length 9 cm internally in the ratio 4 : 3. Also, give justification of the construction.**

**Solution:**

**Steps of construction :**

(i)Draw a line segment AB = 9 cm.

(i)

**(ii)**Draw a ray AX making an acute angle with AB.

**(iii)**From B, draw another ray BY parallel to AX.

**(iv)**Cut off 4 equal parts from AX and 3 parts from BY.

**(v)**Join 4 and 3 which intersects AB at P.

P is the required point which divides AB in the ratio of 4 : 3 internally.

**Question 3.
**

**Divide a line segment of length 14 cm internally in the ratio 2 : 5. Also justify your construction.**

**Solution:**

**Steps of construction :**

(i)Draw a line segment AB = 14 cm.

(i)

**(ii)**Draw a ray AX making an acute angle with AB.

**(iii)**From B, draw another ray BY parallel to AX.

**(iv)**From AX, cut off 2 equal parts and from B, cut off 5 equal parts.

**(v)**Join 2 and 5 which intersects AB at P.

P is the required point which divides AB in the ratio of 2 : 5 internally.

**Question 4.
**

**Draw a line segment of length 8 cm and divide it internally in the ratio 4 : 5.**

**Solution:**

**Steps of construction :**

(i)Draw a line segment AB = 8 cm.

(i)

**(ii)**Draw a ray AX making an acute angle with ∠BAX = 60° withAB.

**(iii)**Draw a ray BY parallel to AX by making an acute angle ∠ABY = ∠BAX.

**(iv)**Mark four points A

_{1}, A

_{2}, A

_{3}, A

_{4}on AX and five points B

_{1}, B

_{2}, B

_{3}, B

_{4}, B

_{s}on BY in such a way that AA

_{1}= A

_{1}A

_{2}= A

_{2}A

_{3}= A

_{3}A

_{4}.

**(v)**Join A

_{4}B

_{5}.

**(vi)**Let this line intersect AB at a point P.

Thus, P is the point dividing the line segment AB internally in the ratio of 4 : 5.

Hope given RD Sharma Class 10 Solutions Chapter 9 Constructions Ex 9.1 are helpful to complete your math homework.

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