question_answer

Suppose point \[D(1,4)\] divide the line segment AB in the ratio \[k:1,\] then find the value of k.

A) \[3\]

B) \[3/2\]

C) \[2\]

D)  \[1/2\]

Correct Answer: B

Solution :

By suing internal section formula.

\[\therefore \]  Coordinates of \[D=\left\{ \frac{3k+(-2)}{k+1},\frac{4k+4}{k+1} \right\}\]

\[\Rightarrow \,\,\,\,\,(1,4)=\left\{ \frac{3k-2}{k+1},\frac{4k+4}{k+1} \right\}\]

On comparing x-coordinate both sides,

\[1=\frac{3k-2}{k+1}\Rightarrow 3k-2=k+1\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2k=3\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,k=\frac{3}{2}\]

So, option [b] is correct.