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Division of a Line Segment

To Divide a Line Segment in a Given Ratio

 

Example

Divide a line segment of length 7 cm in the ratio 3:5 internally.

Solution

Steps of Construction
 


1. Draw a line segment AB = 7 cm.

2. Draw a ray AX making an acute angle BAX with AB.

3. Along AX, mark off 8( = 3 + 5) points A1, A2, A3, A4, A5, A6, A7 and A8 such that AA1  

=A1A2 = A2A3 = A3A4 = A4A5 = A5A6 = A6A7 = A7A8

4. Join A8 to B.

5. Through A3, draw a line A||AB intersecting AB at P.

The point P is the desired point which divides AB internally in the ratio of 3 : 5.


 

Example

Divide a line segment of 5 cm length externally in the ratio of 2 : 3.

Solution

Steps of Construction


1. Draw the line segment AP = 5 cm.

2. Draw a ray AC making an acute angle BAC with AB.

3. Along AC mark off 5 (equal to bigger number of ratio) points A1,A2,A3,A4, and A5 such that AA1  =A1A2 = A2A3 = A3A4 = A4A5.

4. Join A2(= 5 - 3)th point to B.

5. Through A5 and parallel to A2B draw a line A5P intersecting the given line AB (produced) in P, P is the required point.





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