Using determinants show that the following points are collinear: … - Vidyadip

Question

Using determinants show that the following points are collinear:
(3, -2), (8, 8) and (5, 2)

✓

Answer

If the points (3, -2), (8, 8) and (5, 2) collinear, then
$\triangle=\begin{vmatrix}3&-2&1\\8&8&1\\5&2&1\end{vmatrix}=0$
$=\begin{vmatrix}3&-2&1\\5&10&0\\5&2&1\end{vmatrix}$ [Applying R₂ → R₂ - R₁]
$=\begin{vmatrix}3&-2&1\\5&10&0\\2&4&0\end{vmatrix}$ [Applying R₃ → R₃ - R₁]
$=\begin{vmatrix}5&10\\2&4\end{vmatrix}$
$=20-20$
$=0$
Thus, points are collinear.

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