Question

To divide a line segment $AB$ in the ratio $3:4$, first a ray $AX$ is drawn so that $\angle BAX$ is an acute angle and then at equal distances points are marked on the ray $AX$ such that the minimum number of these points is:

• A. $5$
• B. $7$
• C. $8$
• D. $9$

Answer 1

The correct option is B $7$

To divide the line segment $AB$ in the ratio $3:4$ at point $D$, the line $AB$ must first be divided into $3+4=7$ equal parts. Then $3$ out of the $7$ parts will lie on one side of $D$ and the remaining $4$ on the other side. Hence, ray $AX$ must be divided into $7$ equal parts.