divide a line segment ab=8cm in the ratio 2:3:4

To divide a line segment of length 8 cm in the ratio 2:3:4, we follow the below given steps.

We draw a line segment PQ of length 8 cm.

Now, we draw a ray PX making an acute angle with PQ and draw a ray QY parallel to PX by making ∠PQY equal to ∠QPX.

Firstly, we locate 5 points P

_{1}, P_{2}, P_{3,}P_{4}, and P_{5}on PX and 4 points Q_{1}, Q_{2}, Q_{3}and Q_{4}on QY such that PP_{1}= P_{1}P_{2}= P_{2}P_{3}= P_{3}P_{4 }= P_{4}P_{5}= QQ_{1}= Q_{1}Q_{2}= Q_{2}Q_{3}= Q_{3}Q_{4}

Now, we join P

_{5}Q_{4}which intersects PQ at S. Therefore, PS : SQ = 5 : 4.- Now, we divide PS in the ratio 2 : 3 by again repeating the same procedure.

6. Now, we draw a ray SZ parallel to PX by making ∠PSZ equal to ∠QPX.

7. Firstly, we locate 2 points P_{1} and P_{2 }on PX and 3 points x_{1}, x_{2 }and x_{3} on SZ such that PP_{1} = P_{1}P_{2} = Sx_{1} = x_{1}x_{2 }= x_{2}x_{3} .

8. Now, we join P_{2}x_{3} which intersects PS at R. Therefore, PR : RS = 2 : 3.

Hence, PR : RS : SQ = 2 : 3 : 4.

Hope you get it!!

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