Question

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

Answer 1

Step of Construction :

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

2. Draw a line from $A$ making an acute angle with line segment $AB$.

3. Taking $A$ as centre draw an arc cutting $A_1$ on the line.

And with the same radius consider $A_1$ as a centre and draw another arc cutting line at $A_2$.

Repeat the same procedure an divide the line $AX$ from $A$ into $8$ equal parts :

$A{A}_1,A_1{A}_2,A_2{A}_3,A_3{A}_4,A_4{A}_5,A_5{A}_6,A_6{A}_7$ and $A_7{A}_8$

4. Join $A_8$ and $B$ by drawing a line.

5. Draw a parallel line to $A_{8}B$ from $A_3$which divides line segment $AB$ at point $P$

6. $P$ is the required point such that $AP/AB=3/5$.