**Answer
1** :

Steps of construction :

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

(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.

**Answer
2** :

Steps of construction :

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

(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.

**Answer
3** :

Steps of construction :

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

(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.

**Answer
4** :

Steps of construction :

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

(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 A1, A2, A3, A4 on AX and five points B1, B2, B3, B4, Bs on BY in such a way that AA1 = A1A2 = A2A3 = A3A4 .

(v) Join A4B5.

(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.

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