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

Question

Using determinants show that the following points are collinear:
(2, 3), (-1, -2) and (5, 8)

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Answer

If given points are collinear, then area of the triangle must be zero.
Hence,
$=\frac{1}{2}\begin{vmatrix}2&3&1\\-1&-2&1\\5&8&1\end{vmatrix}$
$=\frac{1}{2}\big[2(-10)-3(-6)+1(2)\big]$
$=\frac{1}{2}[-20+18+2]$
$=\frac{1}{2}[0]$
$=0$
Hence the given points are collinear.

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