Question:
Draw a line segment $A B$ of length $7 \mathrm{~cm}$. Using ruler and compasses, find a point $P$ on $A B$ such that $\frac{A P}{A B}=\frac{3}{5}$.
Solution:
Steps of Construction:
Step 1. Draw a line segment AB = 7 cm.
Step 2. Draw a ray AX, making an acute angle
Step 3. Along AX, mark 5 points (greater of 3 and 5) A1, A2, A3, A4 and A5 such that
AA1 = A1A2 = A2A3 = A3A4 = A4A5
Step 4. Join A5B.
Step 5. From A3, draw A3P parallel to A5B (draw an angle equal to
Here, $\mathrm{P}$ is the point on $\mathrm{AB}$ such that $\frac{\mathrm{AP}}{\mathrm{PB}}=\frac{3}{2}$ or $\frac{\mathrm{AP}}{\mathrm{AB}}=\frac{3}{5}$.