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.
$\begin{vmatrix} 9 & 5 & 1 \\1 & 2 & 1 \\a & 8 & 1\end{vmatrix}=0$
Applying operation $R_{2} \rightarrow R_{2}-R_{1}, R_{3} \rightarrow R_{3}-R_{1}$, we get
$\begin{vmatrix}9 & 5 & 1 \\-8 & -3 & 0 \\a-9 & 3 & 0\end{vmatrix}=0$
Expanding along $C_{3}$, we get
$-24+3(a-9)=0 $
$\Rightarrow \, 3 a-51=0$
$ \Rightarrow \,a=17$