No restriction on base orientation. For every pair of points, compute slope k=dy/dx. Lines with same slope but different intercept b are parallel — they form trapezoid sides.

For each slope k, group by intercept b. Number of parallel-line pairs = C(count_of_intercepts, 2). Sum over all slopes. Then subtract parallelograms (counted twice): group by midpoint, for each midpoint sum C(count_per_slope, 2).

Handle vertical lines (dx=0) with sentinel slope value. Use double for k and b — watch for -0.0 vs 0.0. O(n²) time, n ≤ 500. Midpoint encoding: (x1+x2+2000)*4000 + (y1+y2+2000) avoids hash collisions.