Question

In what ratio does the point $C(\frac{3}{5},\frac{11}{5})$ divide the line segment joining the points $A(3,5)$ and $B(-3,-2)$.

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

Answer 1

The correct option is D $2:3$

Let the point $C(\frac{3}{5},\frac{11}{5})$ divides the points $A(3,5)$ and $B(-3,-2)$ in ratio $m:1$.

By section formula:

$x=\frac{m{x}_2+n{x}_1}{m+n}$

$\Rightarrow \frac{3}{5}=\frac{3-3m}{m+1}$

$\Rightarrow 3m+3=15-15m$

$\Rightarrow 18m=12$

$\Rightarrow m=\frac{2}{3}$.

Hence, the required ratio is $2:3$.