Question

Given a line segment $AB$. We want to divide it in the ratio $m:n$ where both $m$ and $n$ are positive integers. To help you to understand it, we shall take $m=3$ and $n=2$.

Which of the following step is not required for construction?

• A. Draw any ray $AX$, making an acute angle with $AB$.
• B. Locate $5(=m+n)$ points $A_1,A_2,A_3,A_4$ and $A_5$ on $AX$ so that $A{A}_1=A_1{A}_2=A_2{A}_3=A_3{A}_4=A_4{A}_5$.
• C. Join $B{A}_5$.
• D. Through the point $A_3(m=3)$, draw a line parallel to $A_{5}B$ (by making an angle equal to $\angle A{A}_{5}B$) at $A_3$ intersecting $AB$ at the point $C$.
• E. None of above

Answer 1

Answer: (E)

None of above

The steps for dividing a line segment into a given ratio are:

1. Draw any ray $AX$, making an acute angle with $AB$.

2. Locate $5(=m+n)$ points $A_1,A_2,A_3,A_4$ and $A_5$ on $AX$ so that $A{A}_1=A_1{A}_2=A_2{A}_3=A_3{A}_4=A_4{A}_5$.

3. Join $B{A}_5$.

4. Through the point $A_3(m=3)$, draw a line parallel to $A_{5}B$ (by making an angle equal to $\angle A{A}_{5}B$) at $A_3$ intersecting $AB$ at the point $C$.

Then, $AC:CB=3:2$

All of these steps are important.

So, option $\left(E\right)$ is correct.