Question

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

• A. 17
• B. 8
• C. 7
• D. 71
• E. 1

Answer 1

Answer: (A)

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
$-24+3(a-9)=0$
$\Rightarrow 3a-51=0$
$\Rightarrow a=17$