Are (-1, 1), (2, 2), and (6, 5) collinear?

Three points (x_{1}, y_{1}), (x_{2},
y_{2}), and (x_{3}, y_{3}) are collinear (lie on the
same line) if and only if

Therefore, with the points (-1, 1), (2, 2), and (6, 5) – we have (expanding on the first row)

Because the value of this determinant is not zero, the three points do not lie on the same line (not collinear).