Division of a line segment

To divide a line segment in a given ratio.

Given a line segment AB, we want to divide it in the ratio m : n, where both m and n are positive integers. To help you to understand it, we shall take m = 3 and n = 2.

Steps of Construction:

Step I : Draw any ray AX, making an acute angle with AB.


Step II :

 Locate 5 (m+n) points A1,A2,A3,A4,  and A5,  on AX so that 

 AA1  = A1A2 = A2A= A3A4  = A4A 

Step III : Join BA5.  

Step IV :

 Through the point A(m=3), draw a line parallel to A5B(by

making an angle equal to ∠AA5)  intersecting AB at the point C (see fig.). Then ,AC : CB = 3 : 2.

Let us see how this method gives us the required division.