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.
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.
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.