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 answer is C)The slope of GH = − 5/ 8 , and the slope of FH = 8/ 5 ; therefore, GH ⊥ FH.

Answer 2

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.