Valid Triangle + Point Inclusion

Requirements

You receive three vertices of a triangle, A(x1,y1), B(x2,y2), and C(x3,y3), along with two points to test: P(xp,yp) and Q(xq,yq).

1. Begin by checking that the three vertices form a valid triangle: their side lengths must meet the strict triangle inequality, meaning, for example, AB + BC > AC; no vertex pair may produce a collinear configuration.
2. Return 0 when the triangle fails validation.
3. For a valid triangle, return the appropriate code:
   • 1 when P lies inside and Q does not,
   • 2 when Q lies inside and P does not,
   • 3 when both query points lie inside,
   • 4 when neither query point lies inside.

public static int pointsBelong(int x1, int y1, int x2, int y2, int x3, int y3,
                               int xp, int yp, int xq, int yq)

Notes

• A point lying exactly on an edge is treated as outside.
• This familiar computational-geometry containment approach is usually enough for online assessments, whose tests rarely examine degeneracies such as collinear triangle vertices or a query point exactly at a vertex; an interviewer may still ask about them.