dividing a given line segment into a given ratio( some any three points)
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Answer
Let AB be our given line segment.
To construct:
Divide AB in the ratio of 3 : 5.
Steps of construction
1) Draw
AB
.
2) Draw
AX
, making an acute angle with AB.
3) Locate 8(= 3 + 5) points A
1
,A
2
,A
3
,A
4
,A
5
,A
6
,A
7
and A
8
on
AX
so that AA
1
=A
1
A
2
=A
2
A
3
=A
3
A
4
=A
4
A
5
=A
5
A
6
=A
6
A
7
=A
7
A
8
.
4) Join BA
8
.
5) Through the point A
3
draw a line parallel to A
8
B
(By making an angle equal to ∠AA
8
B) at A
3
intersecting AB at the point C.
Then AC : CB = 3 : 5.
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