Question

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

Answer 1

Steps of construction:

1) Draw a line segment AB = 8 cm.

2) Draw a ray AX making an acute angle $\angle BAX=60°$ with AB.

3) Draw a ray BY parallel to AX by making an acute angle $\angle ABY=\angle BAX$.

4) Mark of four points $A_1,A_2,A_3,A_4$ on AX and five points $B_1,B_2,B_3,B_4,B_5$ on BY in such a way that $A{A}_1=A_1{A}_2=A_2{A}_3=A_3{A}_4$.

5) Joins $A_4{B}_5$ and this line intersects AB at a point P.

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