If the points (3, -2), (x, 2), (8, 8) are collinear, find x using… - Vidyadip

Question

If the points (3, -2), (x, 2), (8, 8) are collinear, find x using determinant.

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Answer

Since the points are collinear, hance the area of the traingle must be zero.
$\Rightarrow\frac{1}{2}\begin{vmatrix}3&-2&1\\\text{x}&2&1\\8&8&1\end{vmatrix}=0$
$\Rightarrow3(-6)+2(\text{x}-8)+1(8\text{x}-16)=0$
$\Rightarrow-18+2\text{x}-16+8\text{x}-16=0$
$\Rightarrow10\text{x}=50$
$\Rightarrow\text{x}=5$
Hence x = 5

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