Question

If the point C(k,4) divides the join of points A(2,6) and B(5,1) in the ratio 2:3, then find the value of k.

Answer 1

We know that by section formula, the co-ordinates of the points which divide internally the line segment joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$ is

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

Given that the point $C(k,4)$ divides the join of $A(2,6)$ and $B(5,1)$ in ration $2:3$.

Therefore,

$k=\frac{2\times 5+3\times 2}{2+3}$

$\Rightarrow k=\frac{10+6}{5}$

$\Rightarrow k=\frac{16}{5}$

Thus the value of $k$ is $\frac{16}{5}$.

Hence the correct answer is $\frac{16}{5}$.