Question

Given that three points $(1,2),(2,4),(k,6)$ are collinear, find the value of $k$.

Answer 1

As Points are collinear

$\Rightarrow$ area of traiangle formed by $3$ Points is zero.

$\Rightarrow \frac{1}{2}\left|\begin{array}{cc}(x_1-x_2)& (x_2-x_3)\\ (y_1-y_2)& (y_2-y_3)\end{array}\right|=0$

$\Rightarrow \left|\begin{array}{cc}1-2& 2-k\\ 2-4& 4-6\end{array}\right|$

$\Rightarrow 2-(k-2)2=0$

$\Rightarrow 1+2-k=0\Rightarrow K=3$