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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:

  1. Draw line AB
  2. Draw any ray AX, making an acute angle ( angle less than 90° ) with AB.
  3. Mark 5 (= 3 + 2 ) points A_1,  A_2,  A_3,  A_4 and A_5 on AX so that 〖AA〗_1=〖A_1 A〗_2=〖A_2 A〗_3=〖A_3 A〗_4=〖A_4 A〗_5  by drawing equal arcs
  4. Join 〖BA〗_5.
  5. Since we want the ratio 3 : 2, Through point A_3 (m = 3) , we draw a line parallel to A_5 B (by making an angle equal to ∠AA5B at A3  intersecting AB at the point C.

Thus, AC : CB = 3 : 2.

Justification

Since A_3 C is parallel to A_5 B, therefore,

  〖AA〗_3/(A_3 A_5 )=AC/CB

By construction, 〖AA〗_3/(A_3 A_5 )=3/2.

Therefore, AC/CB=3/2.

This shows that C divides AB in the ratio 3 : 2.

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  1. Chapter 11 Class 10 Constructions
  2. Concept wise
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Transcript

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 𝐴_1, 𝐴_2, 𝐴_3, 𝐴_4 and 𝐴_5 on AX so that 〖𝐴𝐴〗_1=〖𝐴_1 𝐴〗_2=〖𝐴_2 𝐴〗_3=〖𝐴_3 𝐴〗_4=〖𝐴_4 𝐴〗_5 by drawing equal arcs Join 〖𝐵𝐴〗_5. Since we want the ratio 3 : 2, Through point 𝐴_3 (m = 3), we draw a line parallel to 𝐴_5 𝐵 (by making an angle equal to ∠AA5B at A3) intersecting AB at the point C. Thus, AC : CB = 3 : 2. Justification In Δ AA5B Since 𝐴_3 𝐶 is parallel to 𝐴_5 𝐵, therefore, 〖𝐴𝐴〗_3/(𝐴_3 𝐴_5 )=𝐴𝐶/𝐶𝐵 By construction, 〖𝐴𝐴〗_3/(𝐴_3 𝐴_5 )=3/2. Therefore, 𝐴𝐶/𝐶𝐵=3/2. This shows that C divides AB in the ratio 3 : 2.

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CA Maninder Singh
CA Maninder Singh is a Chartered Accountant for the past 7 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .
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