Triangles and straight lines

You will write three functions: the area of a triangle from its vertices, a test for collinear points and the coefficients of the line through two points. The checker tests many cases.

The idea. The determinant with rows $(x_i, y_i, 1)$ is $x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)$. Half its absolute value is the area. The line through $(x_1, y_1)$ and $(x_2, y_2)$ is $Ax + By + C = 0$ with $A = y_1 - y_2$, $B = x_2 - x_1$ and $C = x_1y_2 - x_2y_1$.

Your tasks.

1. Finish area(p, q, r). Each point is a pair (x, y).
2. Finish collinear(p, q, r). Return True if the three points are on one line.
3. Finish line(p, q). Return the triple (A, B, C).