Question

Draw a line segment of length 7 cm and divide it internally in the ratio 2 : 3.

Answer 1

Given that

Determine a point which divides a line segment of length 7 cm internally in the ratio of 2 : 3.

We follow the following steps of construction

Step of construction

Step: I- First of all we draw a line segment AB = 7 cm

Step: II- We draw a ray AX making an acute angle ${\displaystyle \angle BAX={60}^{\circ }}$ with AB.

Step: III- Draw a ray BY parallel to AX by making an acute angle ${\displaystyle \angle ABY=\angle BAX}$

Step IV - Mark of two points ${\displaystyle A_1,A_2}$ on AX and three points ${\displaystyle B_1,B_2,B_3}$on BY in such a way that ${\displaystyle {\text{AA}}_1=A_1{A}_2=B{B}_1=B_1{B}_2=B_2{B}_3}$

Step V - Join ${\displaystyle A_2{B}_3}$ and this line intersects AB at a point P

Thus P is the point dividing AB internally in the ration of 2:3