Question

The line segment joining the points $A(3,2)$ and $B(5,1)$ is divided at the point P in the ratio $1:2$ and it lies on the line $3x-18y+k=0.$ Find the value of $k$.

Answer 1

Given that point divides the line segment joining the points A(3,2) and B(5,1) in the ratio 1:2

The coordinate of P is ,

By section formula

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

here m:n =1:2,$(x_1,y_1)=(3,2)and(x_2,y_2)=(5,1)$

$\therefore$ $(\frac{1\times 5+2\times 3}{1+2},\frac{1\times 1+2\times 2}{1+2})=(\frac{11}{3},\frac{5}{3})3\left(\frac{11}{3}\right)-18\left(\frac{5}{3}\right)+K=0$

$K-19=0$ $\Rightarrow$ $K=19$