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in Mathematics by (20 points)
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Determine if the point(5,–2),(2,3)and (–2,–11) are collinear

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1 Answer

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by (710 points)

Area of triangle passing through points (5, -2), (2, 3) & (-2, -11) is

\(=\frac{1}{2}\begin{vmatrix}5 & -2 & 1\\2 & 3 & 1\\-2 & -11 & 1\end{vmatrix}\)

\(=\frac{1}{2}\)(5(3 + 11) + 2(2 + 2) + 1(-22 + 6))

\(=\frac{1}{2}\)(70 + 8 - 16)

\(=\frac{1}{2}\) \(\times\) 62

= 31

Hence, given points forms a triangle.

Therefore, they are not collinear.

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