Question

To divide a line segment $AB$ in the ratio $4:5$, a ray $AX$ is drawn first such that $\angle BAX$ is an acute angle and then points $A_1,A_2,...$ are located at equal distances on the ray $AX$ and the point $B$ is joined to

• A. $A_4$
• B. $A_5$
• C. $A_7$
• D. $A_9$

Answer 1

The correct option is D $A_9$

The maximum number of points$=4+5=9$

In this process, once line $AX$ is drawn, it is divided into $9$ equal parts.

The points are marked from point $A$ towards $X$. The last point is then joined to point $B$ to form line $XB$ and passing through the points that were marked on $AX$. These lines can be drawn using set squares to ensure they are parallel.

These parallel lines divide line $AB$ into $9$ equal parts. So, to divide the line in the ratio $4:5$, the first $4$ portions will be taken and last $5$ left as shown. $\therefore$ Answer $=A_9$