Question

If the line segment joining $(2,3)$ and $(-1,2)$ is divided internally in the ratio $3:4$ by the line $x+2y=k,$ then $k$ is :

• A. $\frac{41}{7}$
• B. $\frac{5}{7}$
• C. $\frac{36}{7}$
• D. $\frac{31}{7}$

Answer 1

The correct option is A $\frac{41}{7}$

If the line segment joining $(x_1,y_1)$ and $(x_2,y_2)$ is divide by internally in the ratio $m_1:m_2$ then the intersection point is
$x=\frac{m_1{x}_2+m_2{x}_1}{m_1+m_2}$
and
$y=\frac{m_1{y}_2+m_2{y}_1}{m_1+m_2}$
so
$x=\frac{3\times (-1)+4\times 2}{3+4}=\frac{5}{7}$
$y=\frac{3\times \left(2\right)+4\times 3}{3+4}=\frac{18}{7}$
this point $(\frac{5}{7},\frac{18}{7})$ lies on given equation of line.
satisfying the equation
$\frac{5}{7}+2\times \frac{18}{7}=k$
$k=\frac{41}{7}$
Hence, option 'A' is correct.