Question

Draw a line segment AB of length 7 cm. Using ruler and compasses, find a point P on AB such that `(AP)/(AB) = 3/5`.

Answer 1

Steps of Construction:
Step 1: Draw a line segment AB = 7 cm
Step 2: Draw a ray AX, making an acute angle ∠BAX.
Step 3: Along AX, mark 5 points (greater of 3 and 5) `A^1, A^2, A^3, A^4  and A^5` such that
`A A_1 = A_1 A_2 = A_ A_3 = A_3 A_4 = A_4 A_5`
Step 4: Join  A₅ B. 
Step 5: From A₃, draw  A₃ P parallel to  A₅B ( draw an angle equal to 5 ∠AA₅  B ), meeting AB in P. 

`"Here, P is the point on AB such that"(AP)/(PB) =3/2 or (AP)/(AB) = 3/5.`