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 = A2A3 = A3A4 = A4A5
Step III : Join BA5.
Step IV :
Through the point A3 (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.