Question

To divide a line segment $AB$ in the ratio $5:7$, 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. 8
• B. 10
• C. 11
• D. 12

Answer 1

The correct option is D

12

Finding the minimum number of marked points:

1. In the procedure of dividing a line segment in a given ratio of $m:n$, first, one has to draw a ray passing through any of the endpoints of the line segment. Make sure that this ray makes an acute angle with the given line segment.
2. In the second step, one has to mark total $m+n$ points on the ray at equal distances.

Therefore, total $5+7=12$ points should be marked on the ray $AX$ at equal distance.

Final Answer:

Hence, option D is correct.