Do They Belong?

Problem Overview

• Determine if triangle abc is non-degenerate and whether points p and q lie on or inside it, then return a scenario code 0–4.
• Input: integer coordinates x1,y1,x2,y2,x3,y3 and p(xp,yp), q(xq,yq), each in [0,2000]; Output: one integer scenario.
• Context: 2D computational geometry, point-in-triangle membership in a coding interview problem.
• Source: Goldman interviews; an interview question testing geometry and boundary cases.