Question

If the points $A,B,C,D$ are collinear and $C,D$ divide $AB$ in the ratios $2:3\text{and}-2:3$ respectively, then the ratio in which $A$ divides $CD$ is:

• A. $5:1$
• B. $2:3$
• C. $3:2$
• D. $1:5$

Answer 1

The correct option is D $1:5$

We know that,
If $C,D$ divides $\overrightarrow{AB}$ harmonically in the ratio $m:n,$ then $A,B$ divides $\overrightarrow{PQ}$ in the ratio $m-n:m+n$
$\therefore A$ divides $\overrightarrow{CD}$ in the ratio $2-3:2+3=-1:5$
$\therefore \frac{CA}{AD}=\frac{1}{5}$