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  4. If the points (3, - 2), (x, 2), (8,8) are collinear, then find the value of x.

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Q. If the points $(3, - 2), (x, 2), (8,8)$ are collinear, then find the value of x.

Determinants

Solution:

Since, the given points are collinear.
$\therefore \quad\frac{1}{2} \left|\begin{matrix}3&-2&1\\ x&2&1\\ 8&8&1\end{matrix}\right|=0$
$\Rightarrow \quad3\left(2-8\right)+2\left(x-8\right)+1\left(8x-16\right)=0$
$\Rightarrow \quad-18+2x-16+8x-16=0$
$\Rightarrow \quad10x=50 \Rightarrow x=5$