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. $5$
• B. $6$
• C. $2$
• D. $3$

Answer 1

The correct option is B $6$

Given line $2x+y=k$ …………………$\left(1\right)$ passes through (h, k) which divides line joining points $(1,1)$ & $(2,4)$ in $3:2$

Using section formulae $h=\frac{6+2}{5}$ & $k=\frac{12+2}{5}$

$(h=8/5)$ & $(k=14/5)$

Now line $\left(1\right)$ passes through (h, k)

$2\times \frac{8}{5}+\frac{14}{5}=k$

$k=\frac{16+14}{5}=\frac{30}{5}=6$

$[k=6]$.