Triangles on a plane

The triangle can be formed by choosing $3$ points out of $9$ points but since $5$ points are collinear choosing three points from them would simply result in a straight line( and not triangle). Thus ways:

$\dbinom 93-\dbinom 53=84-10=\boxed{74}$

Other way to think...

Consider 0 points taken from collinear, 3 from non collinear , no. Of ways=4C3=4

Consider 1 point taken from collinear, 2 from non collinear,no. Of ways=5C1×4C2=5×6=30

Consider 2 points then from collinear,1 from non collinear, no of ways=5C2×4C1=10×4=40

Total ways =74

No other ways possible because taking 3 from collinear will become a degenerated triangle