Question

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

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

Answer 1

Answer: (A)

$\frac{5}{7}$

Let $(2,3)$ and $Q(-1,2)$

Refer image,

Ratio is $3:4=m:n$

By section formula we know that

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

$R=(\frac{3\times -1+4\times 2}{3+4},\frac{3\times 2+4\times 3}{3+4})$

$R=(\frac{5}{7},\frac{18}{7})$

now R lies on line $x+2y=k$ so putting value of x and y

$\frac{5}{7}+2\times \frac{18}{7}=\frac{41}{7}=k$

So option (D) is correct.