Respuesta :

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

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