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  1. Class 10
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Construction 11.1 : To divide a line segment in a given ratio. Let us divide a line segment B into 3:2 ratio. Steps of construction: Draw line AB Draw any ray AX, making an acute angle (angle less than 90 ) with AB. Mark 5 (= 3 + 2) points _1, _2, _3, _4 and _5 on AX so that _1= _1 _2= _2 _3= _3 _4= _4 _5 by drawing equal arcs Join _5. Since we want the ratio 3 : 2, Through point _3 (m = 3), we draw a line parallel to _5 (by making an angle equal to AA5B at A3) intersecting AB at the point C. Thus, AC : CB = 3 : 2. Justification In AA5B Since _3 is parallel to _5 , therefore, _3/( _3 _5 )= / By construction, _3/( _3 _5 )=3/2. Therefore, / =3/2. This shows that C divides AB in the ratio 3 : 2.

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.