Question

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

Answer 1

6

Answer 2

The point dividing the segment joining $(1,1)$ and $(2,4)$ in the ratio $3:2$ is $\left(\frac{3(2)+2(1)}{3+2}, \frac{3(4)+2(1)}{3+2}\right) = \left(\frac{8}{5}, \frac{14}{5}\right)$. Substituting this into $2x+y=k$ gives $2\left(\frac{8}{5}\right) + \frac{14}{5} = \frac{16+14}{5} = \frac{30}{5} = 6$.