Chapter- construction 
Ques= Draw a line segment of length 6.5 cm. Find a point P on it which divides it in the ratio 3:2
 

Dear Student,

Please find below the solution to the asked query:
$$\begin{gathered} \mathrm{Step}1=\mathrm{Draw} \mathrm{a} \mathrm{line} \mathrm{segment} \mathrm{of} \mathrm{length} 6.5\mathrm{cm} \\ \mathrm{Step}2=\mathrm{Draw} \mathrm{a} \mathrm{ray} \mathrm{PX} \mathrm{making} \mathrm{an} \mathrm{acute} \mathrm{angle} \mathrm{with} \mathrm{PQ} \mathrm{and} \mathrm{draw} \mathrm{A} \mathrm{QY} \mathrm{parallel} \mathrm{to} \mathrm{PX} \mathrm{by} \mathrm{making} \angle \mathrm{PQY}=\angle \mathrm{QPX} \\ \mathrm{Step}3=\mathrm{Locate} 3 \mathrm{points} {\mathrm{P}}_1,{\mathrm{P}}_2,{\mathrm{P}}_3 \mathrm{on} \mathrm{PX} \mathrm{and} 2 \mathrm{points} {\mathrm{Q}}_1,{\mathrm{Q}}_2 \mathrm{on} \mathrm{QY} \mathrm{such} \mathrm{that} {\mathrm{PP}}_1={\mathrm{PP}}_2={\mathrm{PP}}_3={\mathrm{QQ}}_1={\mathrm{QQ}}_2 \\ \mathrm{Step}4=\mathrm{Now} \mathrm{join} {\mathrm{P}}_3{\mathrm{Q}}_{2 }\mathrm{which} \mathrm{intersects} \mathrm{PQ} \mathrm{at} \mathrm{R} \end{gathered}$$

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