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 )

A right triangle has the two legs that form an angle of 90°, which means that the two legs are perpendicular.

In order to prove that FGH is a right triangle, you need to calculate the slopes of the lines passing through its vertexes and see if there is a pair of opposite reciprocals:

m = (y₂ - y₁) / (x₂ - x₁)

m(FG) = (-9 - 4) / (5 - 2) = -13/3
m(FH) = (-4 - 4) / (-3 - 2) = 8/5
m(HG) = (-4 -(-9)) / (-3 - 5) = -5/8

Since m(FH) and m(HG) are opposite reciprocals, FH is perpendicuar to HG and FGH is a right triangle.