Answer: L, M, N are not collinear.
Three points are collinear if the sum of two of the distances equals the third.
\[LM=\sqrt{3^2+(-6)^2}=\sqrt{45}=3\sqrt5\approx6.71\]
\[MN=\sqrt{4^2+7^2}=\sqrt{65}\approx8.06\]
\[LN=\sqrt{7^2+1^2}=\sqrt{50}=5\sqrt2\approx7.07\]
The largest is \(\sqrt{65}\approx8.06\), but \(LM+LN\approx13.78\ne MN\). No sum of two distances equals the third, so the points are not collinear.