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.

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

Applying $R_2\to R_2-R_{1}and{R}_3\to R_3-R_1$, we get

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

Expanding along $C_3$, we get

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

$\therefore 4k=\frac{40}{7}$