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 ) A) The slope of GH = 5 8 , and the slope of FH = 8 5 ; therefore, GH ⊥ FH. B) The slope of FG = − 5 8 , and the slope of GH = 5 8 ; therefore, FG ⊥ GH. C) The slope of GH = − 5 8 , and the slope of FH = 8 5 ; therefore, GH ⊥ FH. D) The slope of GH = − 8 5 , and the slope of FH = − 5 8 ; therefore, GH ⊥ FH.

Answer 1

The equation of the slope is given by:
m = (y2 - y1) / (x2 - x1)
For GH we have:
m = (-4 - (-9)) / (-3 - 5)
m = (5) / (-8)
m = -5 / 8
For FH we have:
m = (-4 - 4) / (-3 - 2)
m = (-8) / (-5)
m = 8/5
Answer:
C) The slope of GH = - 5/8, and the slope of FH = 8/5; therefore, GH ⊥ FH