Answer: A, B, C are collinear.
Three points are collinear if the sum of two of the distances equals the third.
\[AB=\sqrt{1^2+(-2)^2}=\sqrt5\]
\[BC=\sqrt{(-6)^2+12^2}=\sqrt{180}=6\sqrt5\]
\[AC=\sqrt{(-5)^2+10^2}=\sqrt{125}=5\sqrt5\]
\(AB+AC=\sqrt5+5\sqrt5=6\sqrt5=BC\), so the points are collinear (A lies between B and C).