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 P1, P2, P3, P4, and P5 on PX and 4 points Q1, Q2, Q3 and Q4 on QY such that PP1 = P1P2 = P2P3 = P3P4 = P4P5 = QQ1 = Q1Q2 = Q2Q3= Q3Q4
Now, we join P5Q4 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 P1 and P2 on PX and 3 points x1, x2 and x3 on SZ such that PP1 = P1P2 = Sx1 = x1x2 = x2x3 .
8. Now, we join P2x3 which intersects PS at R. Therefore, PR : RS = 2 : 3.
Hence, PR : RS : SQ = 2 : 3 : 4.
Hope you get it!!