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

Question

Using determinants show that the following points are collinear:
$(5, 5), (-5, 1)$ and $(10, 7)$

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Answer

If 3 points are collinear, then the area of the triangle then form will be zero.
Hence, $\frac{1}{2}\begin{vmatrix}5&5&1\\-5&1&1\\10&7&1\end{vmatrix}=0$
Expanding along $R_1$
$=\frac{1}{2}\big[5(-6)-5(-15)+1(-35-10)]$
$=\frac{1}{2}[-35+75-45]$
$=\frac{1}{2}[0]$
$=0$
Since the area of the triangle is zero, hence the points are collinear.

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