Construction 11.1
To divide a line segment in a given ratio.
Let us divide a line segment AB into 3:2 ratio.
Steps of construction:
Draw line segment AB
Draw any ray AX,
making an acute angle (angle less than 90Β°) with AB.
Mark 5 (= 3 + 2) points π΄_1, π΄_2, π΄_3, π΄_4 and π΄_5 on AX, so that
γπ΄π΄γ_1=γπ΄_1 π΄γ_2=γπ΄_2 π΄γ_3=γπ΄_3 π΄γ_4=γπ΄_4 π΄γ_5 by drawing equal arcs
Join γπ΅π΄γ_5.
Since we want the ratio 3 : 2,
Through point π΄_3 (m = 3), we draw a line parallel to π΄_5 π΅
by making β AA5B = β AA3C
So, we copy β AA5B from point A3
Thus, AC : CB = 3 : 2.
Justification
Since β AA5B = β AA3C,
So, for lines A3C and A5B, with AX as transversal,
corresponding angles are equal
β΄ A3C is parallel to A5B
Now,
Since π΄_3 πΆ is parallel to π΄_5 π΅,
γπ΄π΄γ_3/(π΄_3 π΄_5 )=π΄πΆ/πΆπ΅
By construction,
γπ΄π΄γ_3/(π΄_3 π΄_5 )=3/2.
Therefore,
π΄πΆ/πΆπ΅=3/2
Thus, C divides AB in the ratio 3 : 2.

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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