Show that the points (a, b+c), (b, c+a) & (c, a+b) are collinear, where a>b>c.

Question

I want the solution with distance formula only, not by assuming area zero.

Answer 1

1) determine distance between first and second points

2) determine distance between second and third points

3) determine distance between first and third point.

If collinear 1) + 2) = 3)