Question

To divide a line segment in ratio $7:6$ by construction, how many minimum no. of points should be marked?

• A. $7$
• B. $6$
• C. $12$
• D. $13$

Answer 1

The correct option is D $13$

The minimum number of points $=7+6=13$

In this process, once line $AX$ is drawn, it is divided into $13$ equal parts using a pair of compass. The points are marked from point $A$ towards $X$. The last point is then joined to point $B$ to form line $XB$.

Lines are then drawn parallel to $XB$ 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 will divide line $AB$ into $13$ equal parts. So, to divide the line in the ratio $6:7$, the first $6$ portions will be taken and the last $7$ left.

$\therefore$ Answer $=13$