Divide a line segment of length 9 cm internally in the ratio 4 : 3. Also, give justification of the construction.

Steps of Construction :


1. Draw any ray AX, making an acute angle with AB.


2. Locate 7 points A1, A2, A3, A4,A5,A6 and A7 on AX so that AA1 = A1A2 = A2A3 = A3A4 = A4A5 = A5A6= A6A7


3. Join BA7.


4. Through the point A4, draw a line parallel to A7B at A4intersecting AB at the point C . Then, AC : CB = 4 : 3.




Justification


Since A4C is parallel to A7B, therefore,


AA4/A4A7 (By the Basic Proportionality Theorem) = AC/CB


AA By construction, AA4/A4A7 Therefore, AC/CB = 4/3


This shows that C divides AB in the ratio 4 : 3.


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