Question

If the line $2x+y=k$ passes through the point which divides the line segment joining the points $(1,1)$ and $(2,4)$ in the ratio $3:2,$ then $k$ equals:

• A. $\frac{11}{5}$
• B. $\frac{29}{5}$
• C. $5$
• D. $6$

Answer 1

The correct option is D $6$

$Point\left(p\right)=\frac{\left(6+2\right)}{5},\frac{\left(12+2\right)}{5}$

$p=\left(\frac{8}{5},\frac{14}{5}\right)$

$p=\left(\frac{8}{5},\frac{14}{5}\right)lieson2x+y=k$

$=2\left(\frac{8}{5}\right)+\frac{14}{5}$

$\therefore k=6$

Hence,

Option $D$ is correct answer.