Valid Triangle + Point Inclusion

Geometry OA: validate that three points form a real triangle, then classify whether each of two query points lies inside it. A coordinate-geometry exercise testing the area-sum invariant. Requirements Given the coordinates of three triangle vertices A(x1,y1), B(x2,y2), C(x3,y3) and two query points P(xp,yp), Q(xq,yq): First validate the triangle: the three side lengths must satisfy the triangle inequality (and any pair must not be collinear, i.e. AB + BC > AC strictly). If the triangle is invalid, return 0. If valid, return: 1 if only P is inside, 2 if only Q is inside, 3 if both are inside, 4 if neither is 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 Inclusion test: a point P is inside triangle ABC iff area(ABC) == area(PAB) + area(PBC) + area(PCA). Compute the signed area with the cross-product formula ½ |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|. Floating-point equality is dangerous — compare areas with a small epsilon (or work entirely in integer arithmetic with 2*area). Boundary semantics ("on the edge" = inside or outside?) are not specified; clarify before coding. This is the standard inclusion-test trick from computational geometry; the OA tests do not probe degenerate cases (collinear vertices, point exactly on a vertex) deeply, but real interviewers may. Preparation Derive the signed-area formula by hand from the determinant; do it twice without notes. Practice the integer-only variant (work with 2*area as an int) — it is the safer form for an interviewer to see.