Question

Draw a line segment AB of length 7 cm. Using ruler and compasses, find a point P on AB such that $\frac{\mathrm{AP}}{\mathrm{AB}}=\frac{3}{5}$. [CBSE 2011]

Answer 1

Steps of Construction:

Step 1. Draw a line segment AB = 7 cm.

Step 2. Draw a ray AX, making an acute angle $\angle$BAX.

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 $\angle$AA₅B), meeting AB in P.



Here, P is the point on AB such that $\frac{\mathrm{AP}}{\mathrm{PB}}=\frac{3}{2}$ or $\frac{\mathrm{AP}}{\mathrm{AB}}=\frac{3}{5}$.