Question

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

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

Answer 1

Answer: (A)

$6$

The point which divides $(1,1)$ and $(2,4)$ in the ratio $3:2$

$x=\frac{m_1{x}_2+m_2{x}_1}{m_1+m_2}$,$y=\frac{m_1{y}_2+m_2{y}_1}{m_1+m_2}$

$m_1=3,m_2=2$

$x_1=1,x_2=2,y_1=1,y_2=4$

$x=\frac{3X2+2X1}{3+2}$

$y=\frac{3X4+2X1}{3+2}$

$x=\frac{8}{5},y=\frac{14}{5}$

Since it passes through $2x+y=k$

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

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

$k=\frac{30}{5}$

$k=6$