# Alternative Method For Division Of A Line Segment Internally In A Given Ratio

## Constructions of Class 10

Use the following steps to divide a given line segment AB internally in a given ration m : n, where m and natural members.

### STEPS OF CONSTRUCTION:

(i) Draw a line segment AB of given length.

(ii) Draw any ray AX making an acute angle ∠BAX with AB.

(iii) Draw a ray BY, on opposite side of AX, parallel to AX making an angle ∠ABY equal to ∠BAX.

(iv) Mark off a points A_{1}, A_{2,}....Am’ on AX and n points B_{1}, B_{2},...Bn on BY such that AA_{1} = A_{1}A_{2} = ...... = A_{m}-1 A_{m }= B_{1}B_{2} = ....B_{n-1}B_{n}.

(v) Join A_{m}B_{n}. Suppose it intersect AB at P.

The point P is the required point dividing AB in the ratio m : n.

**question 1.** Decide a line segment of length 6 cm internally in the ratio 3:4.

**Solution: **Follow the following steps :

### STEPS OF CONSTRUCTION:

(i) Draw a line segment AB of length 6 cm.

(ii) Draw any ray AX making an acute angle ∠BAX with AB.

(iii) Draw a ray BY parallel to AX by making ∠ABY equal to ∠BAX.

(iv) Mark of three point A_{1},A_{2},A_{3} on AX and 4 points B1, B2m B3, B4 on BY such that AA_{1} = A_{1}A_{2} = A_{2}A_{3} = BB_{1} = B_{1}B_{2} = B_{2}B_{3} = B_{2}B_{4}.

(v) Join A_{3}B_{4}. Suppose it intersects AB at a point P.

Then, P is the point dividing AB internally in the ratio 3:4.