rmf = RegionMember@Triangle[{{1,2},{3,5},{5,7}}];

pts = RandomReal[7, {10^3, 2}];

Tally[rmf @ pts]

Graphics[{
    Red, Point[Pick[pts, rmf@pts, False]],
    Blue, Point[Pick[pts, rmf@pts, True]],
    Black, RegionBoundary@Triangle[{{1,2},{3,5},{5,7}}]
}]

RegionMember[Triangle[{{1,2},{3,5},{5,7}}], {x, y}]