Are the points (1, 1), (2, 3) and (8, 11) collinear? - Vidyadip

Question

Are the points $(1, 1), (2, 3)$ and $(8, 11)$ collinear$?$

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Answer

Area of triangle formed by these vertices is,
$\triangle=\frac{1}{2}\begin{vmatrix}1&1&1\\2&3&1\\8&11&1\end{vmatrix}$
Applying $R_2 \rightarrow R_2 − R_1, R_{3 }\rightarrow R_{3 }− R_1$
$\triangle=\frac{1}{2}\begin{vmatrix}1&1&1\\1&2&0\\7&10&0\end{vmatrix}=\frac{1}{2}(10-14)=2$
Hence points are non collinear

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