If the line $2 x+y=k$ passes through the point which divides the line segment joining the points $(1,1)$ and…
If the line $2 x+y=k$ 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
$\frac{29}{5}$
$5$
$6$
$\frac{11}{5}$
Solution
Point $p=\left(\frac{6+2}{5}, \frac{12+2}{5}\right)$
$\mathrm{p}=\left(\frac{8}{5}, \frac{14}{5}\right)$
$p\left(\frac{8}{5}, \frac{14}{5}\right)$ lies on $2 x+y=k \quad \Rightarrow \frac{16}{5}+\frac{14}{5}=k \quad \Rightarrow k=\frac{30}{5}=6$