Question

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 )

Answer 1

The slope of GH= -5/8, and the slope of FH=8/5, therefore, GH | FH

Answer 2

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.