Question

If the points $(2, -3), (k, - 1)$ and $(0,4)$ are collinear, then find the value of $4k$.

• A. $4$
• B. $7/140$
• C. $47$
• D. $40/7$

Answer 1

Answer: (D)

The given points are collinear.

$\therefore \quad\frac{1}{2} \left|\begin{matrix}2&-3&1\\ k&-1&1\\ 0&4&1\end{matrix}\right|=0$

Applying $R_{2}\rightarrow R_{2}- R_{1} and R_{3} \rightarrow R_{3} - R_{1}$, we get

$\left|\begin{matrix}2&-3&1\\ k-2&2&0\\ -2&7&0\end{matrix}\right|=0$

Expanding along $C_{3}$, we get

$\Rightarrow \quad\left(k-2\right)7+4=0 \Rightarrow k=\frac{10}{7}$

$\therefore \quad4k=\frac{40}{7}$