Question

To divide a line segment in the ratio $p:q$ ($p,q$ are integers) a ray $AX$ is drawn so that $\angle BAX$ is an acute angle and then mark points on ray $AX$ at equal distances such that the minimum number of points is:

• A. $pq$
• B. $p+q-1$
• C. $p+q$
• D. Greater of $p$ and $q$

Answer 1

The correct option is C $p+q$

Divide the line in $n$ number of points (equidistant)

$n=p+q$

At the nth point, join the end of line segment. At the beginning of line segment $A$ of line segment $AB$, draw a line parallel to that from $N$ cutting the original line segment $AB$

$\therefore$ The minimum number of points required $=p+q$