The coordinates of triangle fgh are f(2, 4), g(5, −9) and h(−3, −4). which statement proves that triangle fgh is a right triangle? (m = y2 - y1 x2 - x1 )

The fact that the slopes of HF and GH are negative reciprocals proves that FGH is a right triangle.

The slope of HF is given by
m = (-4-4)/(-3-2) = -8/-5 = 8/5

The slope of GH is given by
m = (-4--9)/(-3-5) = (-4+9)/(-3-5) = 5/-8 = -5/8

These are reciprocals and opposite sides.  This only occurs if the lines are perpendicular; thus they make a right angle.