Question

The value of $a$, for which the points $(9,5),(1,2)$ and $(a,8)$ are collinear, is

• A. $17$
• B. $8$
• C. $7$
• D. $71$
• E. $1$

Answer 1

The correct option is A $17$

Given, points $(9,5),(1,2)$ and $(a,8)$ are collinear.
$\left|\begin{array}{ccc}9& 5& 1\\ 1& 2& 1\\ a& 8& 1\end{array}\right|=0$
Applying operation $R_2\to R_2-R_1,R_3\to R_3-R_1$ we get
$\left|\begin{array}{ccc}9& 5& 1\\ -8& -3& 0\\ a-9& 3& 0\end{array}\right|=0$
Expanding along $C_3$, we get
$-24+3(a-9)=0$
$\Rightarrow 3a-51=0\Rightarrow a=17$.