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

Answer 1

The correct option is C $6$

Using the section formula, if a point $(x,y)$ divides the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$, then

$(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

Let the point be $G(h,k^{\prime })$. Then the co-ordinates of the point will be given by section formula.
$G(h,k^{\prime })=\frac{2\left(1\right)+3\left(2\right)}{3+2},\frac{2\left(1\right)+3\left(4\right)}{3+2}$
$=\frac{8}{5},\frac{14}{5}$
Since the line passes through G, we get
$2\left(\frac{8}{5}\right)+\frac{14}{5}=k$
$k=\frac{16+14}{5}$
$k=\frac{30}{5}$
$k=6$